A148889 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, -1, 0), (-1, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 31, 98, 384, 1379, 5717, 21582, 90906, 359436, 1547240, 6258149, 27323155, 113033282, 498661277, 2092486392, 9327901281, 39645561390, 177854351272, 763667457504, 3450340919326, 14937583213856, 67807946682328, 295790450043688, 1349191798558525, 5920525724252995, 27107975658796661

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, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A323775 A360605 A119838 * A148890 A148891 A148892

Adjacent sequences: A148886 A148887 A148888 * A148890 A148891 A148892

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved