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 A150500 #23 Apr 20 2025 03:48:22
%S A150500 1,2,7,25,101,416,1787,7792,34645,155722,707795,3242515,14963665,
%T A150500 69458000,324102287,1519028843,7147771981,33750528146,159860887355,
%U A150500 759295147045,3615520821281,17255165910632,82521746019487,395404081034830,1897886817388201,9124229781131546,43930513066698367,211803668881914847
%N A150500 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, -1, 1), (0, 1, 0), (1, 1, -1), (1, 1, 1)}.
%H A150500 Alin Bostan and Manuel Kauers, <a href="https://arxiv.org/abs/0811.2899">Automatic Classification of Restricted Lattice Walks</a>, arXiv:0811.2899 [math.CO], 2008-2009.
%H A150500 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.
%F A150500 a(n) = (A201805(n+1) + 3*A201805(n))/4. - _Mark van Hoeij_, Nov 29 2024
%t A150500 aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
%Y A150500 Cf. A201805.
%K A150500 nonn,walk
%O A150500 0,2
%A A150500 _Manuel Kauers_, Nov 18 2008