The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #4 Dec 28 2023 23:58:07
%S 1,2,7,26,106,441,1913,8405,37758,170982,784866,3623326,16879640,
%T 78965889,371797947,1756213725,8335157567,39660909579,189405764982,
%U 906414415367,4350153987934,20913639508721,100775558575863,486305001210289,2351158641458940,11381247702362433,55179764580772287,267812212122830377
%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, 0), (0, -1, 0), (0, 1, -1), (0, 1, 0), (1, 0, 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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, 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