A148063 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, -1, 1), (-1, 1, -1), (0, 1, 1), (1, -1, -1)}.

1, 1, 2, 3, 12, 25, 77, 181, 716, 1829, 6571, 18269, 70996, 201473, 781810, 2337483, 9127008, 27781965, 110943651, 346119897, 1377659748, 4386994929, 17681473032, 57009873027, 230888035146, 756580283257, 3072648844241, 10174862781405, 41615444481006, 139228467433317, 570476590959141, 1927512584564957

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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

Crossrefs

Sequence in context: A148060 A148061 A148062 * A148064 A148065 A148066

Adjacent sequences: A148060 A148061 A148062 * A148064 A148065 A148066

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved