This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A302180 #23 Nov 05 2024 05:41:18 %S A302180 1,1,3,7,23,71,251,883,3305,12505,48895,193755,783355,3205931, %T A302180 13302329,55764413,236174933,1008773269,4343533967,18834033443, %U A302180 82201462251,360883031291,1592993944723,7066748314147,31493800133173,140953938878821,633354801073571,2856369029213263 %N A302180 Number of 3D walks of type aad. %C A302180 See Dershowitz (2017) for precise definition. %C A302180 Number of 3D walks of length n in the first octant using steps (1, 1, 0), (1, -1, 0), (1, 0, 1), (1, 0, -1) and (1, 0, 0) that start at the origin and end at (n, 0, 0). The analogous problem in 2D is given by the Motzkin numbers A001006. - _Farzan Byramji_, Mar 06 2021 %C A302180 Inverse binomial transform of A145867 (Number of 3D walks of type aae). - _Mélika Tebni_, Nov 05 2024 %H A302180 Nachum Dershowitz, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Dershowitz/dersh3.html">Touchard's Drunkard</a>, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5. %p A302180 M := n-> add(binomial(n, 2*k)*binomial(2*k, k)/(k+1), k = 0 .. iquo(n,2)): # Motzkin numbers %p A302180 A302180 := n-> add((-1)^(n-k)*binomial(n, k)*add(binomial(k, j)*M(j)*M(k-j), j=0..k), k=0..n): seq(A302180(n), n = 0 .. 26); # _Mélika Tebni_, Nov 05 2024 %Y A302180 Cf. A000108, A000984, A001006, A002212, A002896, A005572, A026375, A064037, A081671, A138547, A145847, A145867, A150500, A202814. %K A302180 nonn,walk %O A302180 0,3 %A A302180 _N. J. A. Sloane_, Apr 09 2018 %E A302180 a(14)-a(26) from _Farzan Byramji_, Mar 06 2021