%I #4 Dec 28 2023 22:32:06
%S 1,2,6,20,76,299,1246,5291,23180,102766,464418,2115781,9761718,
%T 45299638,212074088,997141485,4718451470,22402002642,106868910086,
%U 511158778549,2453901475690,11805274313163,56957327738323,275279817557115,1333530890867209,6469275458458120,31443031209732966,153009244617227957
%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), (0, 1, 1), (0, 1, 1), (0, 1, 0), (1, 0, 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, j, k, 1 + n] + aux[i, 1 + j, k, 1 + n] + aux[i, 1 + j, 1 + k, 1 + n] + aux[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
