A148560 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, 0), (-1, 0, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 6, 18, 50, 150, 492, 1539, 5371, 17944, 63704, 225744, 810809, 2983535, 10917690, 40972337, 153287379, 581820688, 2219375147, 8508412508, 32915586038, 127540927543, 498239905499, 1950902335531, 7679230505707, 30343172222925, 120261715941901, 478693474593309, 1909728214904899

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A187124 A369530 A161006 * A148561 A123891 A148562

Adjacent sequences: A148557 A148558 A148559 * A148561 A148562 A148563

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved