A148125 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, 0), (0, 1, 0), (1, -1, -1), (1, -1, 0)}.

1, 1, 2, 4, 11, 26, 75, 214, 661, 1991, 6436, 21020, 69748, 233784, 807658, 2805835, 9816299, 34870101, 125488394, 452757999, 1647072420, 6060766185, 22413227647, 83169470122, 311182120714, 1171769482106, 4423564546452, 16779152505269, 64043346327139, 245222510217633, 941508764962429, 3632252471106596

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, 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: A148122 A148123 A148124 * A148126 A148127 A148128

Adjacent sequences: A148122 A148123 A148124 * A148126 A148127 A148128

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved