The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #4 Dec 28 2023 23:49:57
%S 1,2,7,27,111,474,2081,9331,42489,195793,910692,4268460,20134127,
%T 95477700,454802895,2174770738,10433966295,50205026645,242188473956,
%U 1170953745475,5672804595144,27531900590553,133837053812043,651554256083783,3176142708313533,15501485931109490,75740052339683311
%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, 0, 1), (1, -1, 0), (1, 1, -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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + 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