A148767 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, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 1, 3, 7, 29, 93, 365, 1229, 5293, 19663, 83229, 311889, 1387721, 5469539, 23973181, 94601473, 428312559, 1746245251, 7805363683, 31773614049, 145453492511, 606234306813, 2744169647749, 11406695266495, 52617379377691, 222752070436123, 1017257444499731, 4292728234222733, 19913292817906255

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, -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, -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: A148764 A148765 A148766 * A171180 A151358 A110613

Adjacent sequences: A148764 A148765 A148766 * A148768 A148769 A148770

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved