A148261 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, 0, -1), (-1, 1, 1), (0, 1, 1), (1, -1, -1)}.

1, 1, 2, 4, 14, 33, 111, 323, 1130, 3510, 12490, 42029, 149629, 528322, 1906203, 6946269, 25366147, 94487341, 350079297, 1321045674, 4970250084, 18923592237, 72192070451, 276836591075, 1068574549042, 4125291940046, 16069172459526, 62472117058596, 244992553910023, 959352168248399, 3781377219898688

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148258 A148259 A148260 * A148262 A148263 A148264

Adjacent sequences: A148258 A148259 A148260 * A148262 A148263 A148264

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved