A151005 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, 0, 1), (0, 1, -1), (1, -1, 1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 38, 177, 823, 3953, 19003, 92593, 451880, 2220395, 10923924, 53945354, 266670612, 1321190761, 6550924502, 32527305279, 161609300887, 803687085750, 3998717143782, 19908167842642, 99153850510870, 494066742281765, 2462601445739490, 12278579512463422, 61236110775014294, 305475906740399446

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A151003 A357547 A151004 * A105484 A151006 A151007

Adjacent sequences: A151002 A151003 A151004 * A151006 A151007 A151008

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved