A148150 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, 0), (-1, 0, 1), (0, 0, 1), (0, 1, -1), (1, -1, 0)}.

1, 1, 2, 4, 11, 30, 91, 280, 929, 3125, 10912, 38716, 141115, 521666, 1961738, 7468828, 28818382, 112367258, 442532489, 1758198902, 7044028427, 28431378496, 115539205449, 472502030716, 1943716565577, 8039163734201, 33416716299543, 139559578867379, 585418557877110, 2465785094190391

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A373760 A063544 A276145 * A219232 A073193 A148151

Adjacent sequences: A148147 A148148 A148149 * A148151 A148152 A148153

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved