A148614 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, -1), (1, 1, 0)}.

1, 1, 3, 6, 21, 55, 190, 566, 2017, 6310, 22819, 74608, 271579, 910758, 3341986, 11432723, 42096370, 146207641, 540521446, 1898301662, 7036732860, 24948540427, 92685827088, 331032848634, 1232269687984, 4428719494363, 16510994401030, 59650167582630, 222703644293082, 808132685517214, 3020733783786233

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, -1 + j, 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, -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: A354734 A112520 A148613 * A148615 A148616 A148617

Adjacent sequences: A148611 A148612 A148613 * A148615 A148616 A148617

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved