# Small-Step Walks: Guessed Asymptotic Equivalents for Coefficients

OEISstep setalgequiv
1A005568Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{32 }{\pi } \frac{4 ^n}{n^{3}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
2A001246Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{8 }{\pi } \frac{4 ^n}{n^{3}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
3A151362Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{3 \sqrt{6 }}{\pi } \frac{6 ^n}{n^{3}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
4A172361Your browser does not support the HTML5 canvas tag.N$\frac{128 }{27 \pi } \frac{8 ^n}{n^{3}}$
5A151332Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{16 \sqrt{2 }}{\pi } \frac{(2 \sqrt{2 }) ^n}{n^{3}} & (n=4p) \\ 0 & (n=4p+1) \\ 0 & (n=4p+2) \\ 0 & (n=4p+3) \end{cases}$
6A151357Your browser does not support the HTML5 canvas tag.N$\frac{2 A ^{3/2} }{\pi } \frac{(2 A ) ^n}{n^{3}}$
7A151341Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{12 \sqrt{3 }}{\pi } \frac{(2 \sqrt{3 }) ^n}{n^{3}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
8A151368Your browser does not support the HTML5 canvas tag.N$\frac{2 B ^{3/2} }{\pi } \frac{(2 B ) ^n}{n^{3}}$
9A151345Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{24 \sqrt{30 }}{25 \pi } \frac{(2 \sqrt{6 }) ^n}{n^{3}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
10A151370Your browser does not support the HTML5 canvas tag.N$\frac{2 \mu ^{3} C ^{3/2} }{\pi } \frac{(2 C ) ^n}{n^{3}}$
11A151341Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{12 \sqrt{3 }}{\pi } \frac{(2 \sqrt{3 }) ^n}{n^{3}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
12A151368Your browser does not support the HTML5 canvas tag.N$\frac{2 B ^{3/2} }{\pi } \frac{(2 B ) ^n}{n^{3}}$
13A151345Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{24 \sqrt{30 }}{25 \pi } \frac{(2 \sqrt{6 }) ^n}{n^{3}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
14A151370Your browser does not support the HTML5 canvas tag.N$\frac{2 \mu ^{3} C ^{3/2} }{\pi } \frac{(2 C ) ^n}{n^{3}}$
15A151332Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{16 \sqrt{2 }}{\pi } \frac{(2 \sqrt{2 }) ^n}{n^{3}} & (n=4p) \\ 0 & (n=4p+1) \\ 0 & (n=4p+2) \\ 0 & (n=4p+3) \end{cases}$
16A151357Your browser does not support the HTML5 canvas tag.N$\frac{2 A ^{3/2} }{\pi } \frac{(2 A ) ^n}{n^{3}}$
17A151334Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{81 \sqrt{3 }}{\pi } \frac{3 ^n}{n^{4}} & (n=3p) \\ 0 & (n=3p+1) \\ 0 & (n=3p+2) \end{cases}$
18A151366Your browser does not support the HTML5 canvas tag.N$\frac{27 \sqrt{3 }}{\pi } \frac{6 ^n}{n^{4}}$
19A138349Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{768 }{\pi } \frac{4 ^n}{n^{5}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$

Nature of the generating series for (vx,vy)=(0,0) and coefficient asymptotics

$A=1+\sqrt2$, \ $B=1+\sqrt3$, \ $C=1+\sqrt6$, \ $\lambda=7+3\sqrt6$, \ $\mu=\sqrt{\frac{4\sqrt6-1}{19}}$

OEISstep setalgequiv
1A005558Your browser does not support the HTML5 canvas tag.N$\frac{8 }{\pi } \frac{4 ^n}{n^{2}}$
2A151392Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{4 }{\pi } \frac{4 ^n}{n^{2}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
3A151478Your browser does not support the HTML5 canvas tag.N$\frac{3 \sqrt{6 }}{2 \pi } \frac{6 ^n}{n^{2}}$
4A151496Your browser does not support the HTML5 canvas tag.N$\frac{32 }{9 \pi } \frac{8 ^n}{n^{2}}$
5A151380Your browser does not support the HTML5 canvas tag.N$\frac{3 }{4 } \sqrt{\frac{3 }{\pi }} \frac{3 ^n}{n^{3/2}}$
6A151450Your browser does not support the HTML5 canvas tag.N$\frac{5 }{16 } \sqrt{\frac{10 }{\pi }} \frac{5 ^n}{n^{3/2}}$
7A148790Your browser does not support the HTML5 canvas tag.N$\frac{8 }{3 \sqrt{\pi }} \frac{4 ^n}{n^{3/2}}$
8A151485Your browser does not support the HTML5 canvas tag.N$\sqrt{\frac{3 }{\pi }} \frac{6 ^n}{n^{3/2}}$
9A151440Your browser does not support the HTML5 canvas tag.N$\frac{5 }{24 } \sqrt{\frac{10 }{\pi }} \frac{5 ^n}{n^{3/2}}$
10A151493Your browser does not support the HTML5 canvas tag.N$\frac{7 }{54 } \sqrt{\frac{21 }{\pi }} \frac{7 ^n}{n^{3/2}}$
11A151394Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{36 \sqrt{3 }}{\pi } \frac{(2 \sqrt{3 }) ^n}{n^{3}} & (n=2p) \\ \frac{54 }{\pi } \frac{(2 \sqrt{3 }) ^n}{n^{3}} & (n=2p+1) \end{cases}$
12A151472Your browser does not support the HTML5 canvas tag.N$\frac{3 B ^{7/2} }{2 \pi } \frac{(2 B ) ^n}{n^{3}}$
13A151437Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{72 \sqrt{30 }}{5 \pi } \frac{(2 \sqrt{6 }) ^n}{n^{3}} & (n=2p) \\ \frac{864 \sqrt{5 }}{25 \pi } \frac{(2 \sqrt{6 }) ^n}{n^{3}} & (n=2p+1) \end{cases}$
14A151492Your browser does not support the HTML5 canvas tag.N$\frac{6 \lambda \mu ^{3} C ^{5/2} }{5 \pi } \frac{(2 C ) ^n}{n^{3}}$
15A151375Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{448 \sqrt{2 }}{9 \pi } \frac{(2 \sqrt{2 }) ^n}{n^{3}} & (n=4p) \\ \frac{640 }{9 \pi } \frac{(2 \sqrt{2 }) ^n}{n^{3}} & (n=4p+1) \\ \frac{416 \sqrt{2 }}{9 \pi } \frac{(2 \sqrt{2 }) ^n}{n^{3}} & (n=4p+2) \\ \frac{512 }{9 \pi } \frac{(2 \sqrt{2 }) ^n}{n^{3}} & (n=4p+3) \end{cases}$
16A151430Your browser does not support the HTML5 canvas tag.N$\frac{4 A ^{7/2} }{\pi } \frac{(2 A ) ^n}{n^{3}}$
17A151378Your browser does not support the HTML5 canvas tag.N$\frac{27 }{8 } \sqrt{\frac{3 }{\pi }} \frac{3 ^n}{n^{5/2}}$
18A151483Your browser does not support the HTML5 canvas tag.Y$\frac{27 }{8 } \sqrt{\frac{3 }{\pi }} \frac{6 ^n}{n^{5/2}}$
19A005568Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{32 }{\pi } \frac{4 ^n}{n^{3}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$

Nature of the generating series for (vx,vy)=(0,1) and coefficient asymptotics

$A=1+\sqrt2$, \ $B=1+\sqrt3$, \ $C=1+\sqrt6$, \ $\lambda=7+3\sqrt6$, \ $\mu=\sqrt{\frac{4\sqrt6-1}{19}}$

OEISstep setalgequiv
1A005558Your browser does not support the HTML5 canvas tag.N$\frac{8 }{\pi } \frac{4 ^n}{n^{2}}$
2A151392Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{4 }{\pi } \frac{4 ^n}{n^{2}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
3A151471Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{2 \sqrt{6 }}{\pi } \frac{6 ^n}{n^{2}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
4A151496Your browser does not support the HTML5 canvas tag.N$\frac{32 }{9 \pi } \frac{8 ^n}{n^{2}}$
5A151379Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{4 \sqrt{2 }}{\pi } \frac{(2 \sqrt{2 }) ^n}{n^{2}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
6A148934Your browser does not support the HTML5 canvas tag.N$\frac{\sqrt{2 }A ^{3/2} }{\pi } \frac{(2 A ) ^n}{n^{2}}$
7A151410Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{4 \sqrt{3 }}{\pi } \frac{(2 \sqrt{3 }) ^n}{n^{2}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
8A151464Your browser does not support the HTML5 canvas tag.N$\frac{2 B ^{3/2} \sqrt{3 }}{3 \pi } \frac{(2 B ) ^n}{n^{2}}$
9A151423Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{4 \sqrt{30 }}{5 \pi } \frac{(2 \sqrt{6 }) ^n}{n^{2}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
10A151490Your browser does not support the HTML5 canvas tag.N$\frac{\sqrt{6 }\mu C ^{3/2} }{3 \pi } \frac{(2 C ) ^n}{n^{2}}$
11A151410Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{4 \sqrt{3 }}{\pi } \frac{(2 \sqrt{3 }) ^n}{n^{2}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
12A151464Your browser does not support the HTML5 canvas tag.N$\frac{2 B ^{3/2} \sqrt{3 }}{3 \pi } \frac{(2 B ) ^n}{n^{2}}$
13A151423Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{4 \sqrt{30 }}{5 \pi } \frac{(2 \sqrt{6 }) ^n}{n^{2}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
14A151490Your browser does not support the HTML5 canvas tag.N$\frac{\sqrt{6 }\mu C ^{3/2} }{3 \pi } \frac{(2 C ) ^n}{n^{2}}$
15A151379Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{4 \sqrt{2 }}{\pi } \frac{(2 \sqrt{2 }) ^n}{n^{2}} & (n=2p) \\ 0 & (n=2p+1) \end{cases}$
16A148934Your browser does not support the HTML5 canvas tag.N$\frac{\sqrt{2 }A ^{3/2} }{\pi } \frac{(2 A ) ^n}{n^{2}}$
17A151497Your browser does not support the HTML5 canvas tag.N$\frac{27 }{8 } \sqrt{\frac{3 }{\pi }} \frac{3 ^n}{n^{5/2}}$
18A151483Your browser does not support the HTML5 canvas tag.Y$\frac{27 }{8 } \sqrt{\frac{3 }{\pi }} \frac{6 ^n}{n^{5/2}}$
19A005817Your browser does not support the HTML5 canvas tag.N$\frac{32 }{\pi } \frac{4 ^n}{n^{3}}$

Nature of the generating series for (vx,vy)=(1,0) and coefficient asymptotics

$A=1+\sqrt2$, \ $B=1+\sqrt3$, \ $C=1+\sqrt6$, \ $\lambda=7+3\sqrt6$, \ $\mu=\sqrt{\frac{4\sqrt6-1}{19}}$

OEISstep setalgequiv
1A005566Your browser does not support the HTML5 canvas tag.N$\frac{4 }{\pi } \frac{4 ^n}{n}$
2A018224Your browser does not support the HTML5 canvas tag.N$\frac{2 }{\pi } \frac{4 ^n}{n}$
3A151312Your browser does not support the HTML5 canvas tag.N$\frac{\sqrt{6 }}{\pi } \frac{6 ^n}{n}$
4A151331Your browser does not support the HTML5 canvas tag.N$\frac{8 }{3 \pi } \frac{8 ^n}{n}$
5A151266Your browser does not support the HTML5 canvas tag.N$\frac1{2 } \sqrt{\frac{3 }{\pi }} \frac{3 ^n}{n^{1/2}}$
6A151307Your browser does not support the HTML5 canvas tag.N$\frac1{4 } \sqrt{\frac{10 }{\pi }} \frac{5 ^n}{n^{1/2}}$
7A151291Your browser does not support the HTML5 canvas tag.N$\frac{4 }{3 \sqrt{\pi }} \frac{4 ^n}{n^{1/2}}$
8A151326Your browser does not support the HTML5 canvas tag.N$\frac{2 }{3 } \sqrt{\frac{3 }{\pi }} \frac{6 ^n}{n^{1/2}}$
9A151302Your browser does not support the HTML5 canvas tag.N$\frac1{6 } \sqrt{\frac{10 }{\pi }} \frac{5 ^n}{n^{1/2}}$
10A151329Your browser does not support the HTML5 canvas tag.N$\frac1{9 } \sqrt{\frac{21 }{\pi }} \frac{7 ^n}{n^{1/2}}$
11A151261Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{12 \sqrt{3 }}{\pi } \frac{(2 \sqrt{3 }) ^n}{n^{2}} & (n=2p) \\ \frac{18 }{\pi } \frac{(2 \sqrt{3 }) ^n}{n^{2}} & (n=2p+1) \end{cases}$
12A151297Your browser does not support the HTML5 canvas tag.N$\frac{\sqrt{3 }B ^{7/2} }{2 \pi } \frac{(2 B ) ^n}{n^{2}}$
13A151275Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{12 \sqrt{30 }}{\pi } \frac{(2 \sqrt{6 }) ^n}{n^{2}} & (n=2p) \\ \frac{144 \sqrt{5 }}{5 \pi } \frac{(2 \sqrt{6 }) ^n}{n^{2}} & (n=2p+1) \end{cases}$
14A151314Your browser does not support the HTML5 canvas tag.N$\frac{\sqrt{6 }\lambda \mu C ^{5/2} }{5 \pi } \frac{(2 C ) ^n}{n^{2}}$
15A151255Your browser does not support the HTML5 canvas tag.N$\begin{cases} \frac{24 \sqrt{2 }}{\pi } \frac{(2 \sqrt{2 }) ^n}{n^{2}} & (n=4p) \\ \frac{32 }{\pi } \frac{(2 \sqrt{2 }) ^n}{n^{2}} & (n=4p+1) \\ \frac{24 \sqrt{2 }}{\pi } \frac{(2 \sqrt{2 }) ^n}{n^{2}} & (n=4p+2) \\ \frac{32 }{\pi } \frac{(2 \sqrt{2 }) ^n}{n^{2}} & (n=4p+3) \end{cases}$
16A151287Your browser does not support the HTML5 canvas tag.N$\frac{2 \sqrt{2 }A ^{7/2} }{\pi } \frac{(2 A ) ^n}{n^{2}}$
17A001006Your browser does not support the HTML5 canvas tag.Y$\frac{3 }{2 } \sqrt{\frac{3 }{\pi }} \frac{3 ^n}{n^{3/2}}$
18A129400Your browser does not support the HTML5 canvas tag.Y$\frac{3 }{2 } \sqrt{\frac{3 }{\pi }} \frac{6 ^n}{n^{3/2}}$
19A005558Your browser does not support the HTML5 canvas tag.N$\frac{8 }{\pi } \frac{4 ^n}{n^{2}}$

Nature of the generating series for (vx,vy)=(1,1) and coefficient asymptotics

$A=1+\sqrt2$, \ $B=1+\sqrt3$, \ $C=1+\sqrt6$, \ $\lambda=7+3\sqrt6$, \ $\mu=\sqrt{\frac{4\sqrt6-1}{19}}$