A148613 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, 0), (-1, 0, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 6, 21, 54, 208, 611, 2491, 7948, 33628, 113525, 492930, 1733922, 7673528, 27851685, 125066046, 465304001, 2113510279, 8022430212, 36778270926, 141937911217, 655676836686, 2566059065958, 11929532572720, 47248484525875, 220846203815072, 883777437652486, 4150091488919481

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A098511 A354734 A112520 * A148614 A148615 A148616

Adjacent sequences: A148610 A148611 A148612 * A148614 A148615 A148616

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved