A148223 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, 1, -1), (1, -1, 0), (1, 0, 1)}.

1, 1, 2, 4, 13, 31, 99, 273, 963, 2801, 10194, 31206, 116785, 370867, 1412074, 4614618, 17876773, 59575335, 233800362, 794034650, 3142364959, 10840573537, 43293590497, 151088558313, 608045728883, 2145543500025, 8681107288912, 30937571154404, 125848861557799, 452038834822295, 1848095142289227

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 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, 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: A148220 A148221 A148222 * A148224 A148225 A148226

Adjacent sequences: A148220 A148221 A148222 * A148224 A148225 A148226

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved