A151209 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, 0), (1, 0, 0), (1, 0, 1), (1, 1, 1)}.

1, 3, 13, 53, 243, 1075, 5051, 23183, 110405, 517269, 2484517, 11792641, 56977377, 272851117, 1324046545, 6381308549, 31069554259, 150465126731, 734529518555, 3570566608175, 17468053878847, 85166550969683, 417399494671519, 2040006648094923, 10013114575982011, 49036845449520447, 241002038724658931

Offset

0,2

Links

Table of n, a(n) for n=0..26.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

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[-1 + i, j, k, -1 + n] + aux[1 + i, j, 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}]

Crossrefs

Sequence in context: A072197 A065838 A052990 * A151210 A151211 A367755

Adjacent sequences: A151206 A151207 A151208 * A151210 A151211 A151212

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved