A149556 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, 1), (-1, 0, 1), (-1, 1, 0), (1, -1, -1), (1, 1, 1)}.

1, 1, 5, 13, 59, 191, 895, 3233, 15359, 58481, 280269, 1108705, 5347725, 21717057, 105256693, 435709221, 2119708801, 8908235721, 43464520833, 184891123055, 904210326399, 3884704463511, 19034796674581, 82461074932553, 404706028422485, 1765690426262411, 8677570221506051, 38090870669380283

Offset

0,3

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, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A149553 A149554 A149555 * A149557 A149558 A149559

Adjacent sequences: A149553 A149554 A149555 * A149557 A149558 A149559

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved