Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #4 Apr 20 2021 14:54:49
%S 1,2,8,33,152,703,3363,16123,78405,382031,1874728,9214167,45464404,
%T 224599699,1112123401,5511828827,27357175892,135878942511,
%U 675540367558,3360357589306,16726611246327,83293809912290,414976379155574,2068124206841016,10310539526314684,51416048094701054,256466352906588744
%N Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1,0,1), (1,-1,1), (1,0,0), (1,1,-1), (1,1,1)}.
%H A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</a>.
%t 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[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
%K nonn,walk
%O 0,2
%A _Manuel Kauers_, Nov 18 2008