A151198 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), (0, 0, -1), (0, 1, 0), (1, 0, 1), (1, 1, 1)}

1, 3, 12, 53, 242, 1123, 5315, 25443, 122624, 594555, 2897359, 14171079, 69507304, 341784562, 1684170321, 8312757257, 41089063126, 203356188085, 1007520250738, 4996268566801, 24796418225814, 123152206270025, 612018222946856, 3043155109702677, 15138997708619128, 75345913512987064

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A138269 A228771 A370023 * A151199 A151200 A151201

Adjacent sequences: A151195 A151196 A151197 * A151199 A151200 A151201

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved