A149816 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, 1), (-1, 1, -1), (0, 0, 1), (1, 0, 0)}.

1, 2, 4, 10, 26, 76, 248, 810, 2710, 9186, 31999, 115123, 418274, 1533038, 5654034, 21106525, 79847876, 304224378, 1165021705, 4480513435, 17346259036, 67616557623, 264822472424, 1040790600976, 4103626251277, 16247011720463, 64588526966231, 257593993547862, 1029967708706396, 4128474717777511

Offset

0,2

Links

Table of n, a(n) for n=0..29.

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, 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] + 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: A047653 A148100 A149815 * A149817 A149818 A148101

Adjacent sequences: A149813 A149814 A149815 * A149817 A149818 A149819

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved