A150356 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, 0, -1), (1, -1, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 7, 23, 91, 350, 1437, 5838, 24751, 104208, 449389, 1929971, 8443469, 36844202, 162713469, 717537441, 3195215965, 14217484796, 63698045653, 285299151193, 1285224654333, 5789830745442, 26195024839731, 118541037429530, 538419893143561, 2446426438959488, 11147832144201953, 50821066170962327

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150353 A150354 A150355 * A150357 A150358 A150359

Adjacent sequences: A150353 A150354 A150355 * A150357 A150358 A150359

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved