A148527 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, 0, -1), (1, -1, -1), (1, 1, 0)}.

1, 1, 3, 5, 19, 39, 155, 369, 1471, 3959, 15459, 46051, 176267, 564455, 2143697, 7174755, 27365581, 93807603, 361787869, 1257350451, 4906289837, 17245735483, 67874546817, 241532985195, 955342193025, 3443976880047, 13661167986099, 49837635543435, 198197145797185, 730015639922845, 2912352174731047

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] + 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: A148524 A148525 A148526 * A148528 A148529 A148530

Adjacent sequences: A148524 A148525 A148526 * A148528 A148529 A148530

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved