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%I #4 Dec 28 2023 20:04:13
%S 1,1,2,3,10,20,63,133,488,1134,4159,9977,38619,96551,380001,972913,
%T 3913896,10241310,41846263,111378893,461040755,1244667953,5208010325,
%U 14229194099,60121447699,165980137990,706675809803,1968160352808,8441479695283,23696553049202,102251059507356,289003009054919,1253963610330642
%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, 0), (-1, -1, 1), (-1, 0, -1), (-1, 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[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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 0,3
%A _Manuel Kauers_, Nov 18 2008