A149980 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), (0, 0, 1), (1, 1, 0)}.

1, 2, 5, 17, 55, 190, 699, 2538, 9573, 36694, 140881, 552275, 2175779, 8624406, 34558783, 138884061, 561597871, 2284073680, 9315683597, 38180167051, 157023821303, 647586013452, 2680241675239, 11120381957470, 46254888597609, 192894174299418, 806020664492243, 3375225373534057

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, 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: A148408 A002692 A148409 * A149981 A149982 A149983

Adjacent sequences: A149977 A149978 A149979 * A149981 A149982 A149983

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved