A150751 - OEIS

%I #5 Nov 05 2025 15:22:15

%S 1,2,8,29,127,528,2405,10591,49296,223989,1056721,4896369,23312282,

%T 109466674,524642598,2487292994,11980610025,57209812926,276644569342,

%U 1328428857274,6444039283829,31081477237993,151163732596780,731737282128490,3566520834933610,17315850275994289,84554376280699649

%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), (-1, 0, 1), (0, 0, 1), (1, 0, -1), (1, 1, 1)}.

%H A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, <a href="https://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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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