A148816 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, 0), (0, 0, -1), (0, 1, 1), (1, -1, 0)}.

1, 1, 3, 8, 26, 89, 317, 1129, 4333, 16375, 64689, 255510, 1031520, 4176411, 17235081, 71002938, 297843534, 1246468199, 5289497067, 22427668932, 96117562882, 411666657671, 1779870206015, 7686833020463, 33480379281149, 145660650014735, 638356364542079, 2795072779720188, 12315985271310940

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A151458 A290351 A148815 * A148817 A148818 A242903

Adjacent sequences: A148813 A148814 A148815 * A148817 A148818 A148819

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved