A148224 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, -1), (-1, 1, 1), (0, -1, -1), (1, 0, 0)}.

1, 1, 2, 4, 13, 31, 99, 291, 933, 2931, 9966, 32366, 111293, 383791, 1324926, 4651886, 16629189, 58774965, 212001926, 771615586, 2789365275, 10229224265, 37832524835, 138930785237, 516591386223, 1933766218507, 7192791482528, 27037450085006, 102219677068259, 384150651788375, 1457047070448317

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, j, k, -1 + n] + aux[i, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + 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: A148221 A148222 A148223 * A148225 A148226 A004644

Adjacent sequences: A148221 A148222 A148223 * A148225 A148226 A148227

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved