The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #4 Jan 02 2024 00:38:41
%S 1,3,9,33,123,459,1767,6795,26397,103323,404439,1591917,6274389,
%T 24780489,98110263,388610895,1541837565,6122129877,24327902433,
%U 96767761083,385038905697,1533118174923,6107008497819,24335988943143,97021648253361,386885931518703,1543276950241995,6157531782523065
%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, -1, -1), (0, 1, 1), (1, 0, 1), (1, 1, 0)}.
%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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[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}]
%K nonn,walk
%O 0,2
%A _Manuel Kauers_, Nov 18 2008