A148412 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, 1), (0, 0, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 5, 17, 57, 199, 713, 2674, 10267, 40224, 159836, 643943, 2624714, 10812420, 44937564, 188217760, 793760602, 3368428829, 14375082907, 61660832974, 265713000488, 1149853946857, 4995201154078, 21777955873016, 95261618979581, 417974121429271, 1839153263761945, 8114102524793937

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[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A148411 A149987 A149988 * A149989 A149990 A149991

Adjacent sequences: A148409 A148410 A148411 * A148413 A148414 A148415

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved