A148526 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, 0, -1), (0, -1, -1), (1, 1, 0)}.

1, 1, 3, 5, 19, 39, 155, 369, 1471, 3959, 15299, 45891, 170211, 558079, 1999887, 7013101, 24643131, 90232963, 316320955, 1182714675, 4196267767, 15761054363, 57083907867, 213546145183, 790981954707, 2943457994735, 11107616249215, 41269813236715, 157573078261155, 587829321797023, 2254898672484591

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, -1 + j, k, -1 + n] + aux[i, 1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148523 A148524 A148525 * A148527 A148528 A148529

Adjacent sequences: A148523 A148524 A148525 * A148527 A148528 A148529

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved