A148122 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, 0), (1, 0, 1)}.

1, 1, 2, 4, 11, 26, 75, 200, 615, 1734, 5496, 16190, 52558, 159708, 527525, 1643716, 5498819, 17440416, 59076866, 190207136, 649511160, 2120878068, 7293205666, 24044898984, 83333951054, 277186873640, 965123750468, 3239821841970, 11330523439496, 38264165578268, 134555828157155, 457066612126410

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, 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, 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: A148119 A148120 A148121 * A148123 A148124 A148125

Adjacent sequences: A148119 A148120 A148121 * A148123 A148124 A148125

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved