A149008 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, 0), (-1, 0, 1), (0, -1, 1), (0, 1, 1), (1, 1, -1)}.

1, 1, 3, 9, 34, 125, 488, 1975, 8084, 33883, 143959, 617600, 2681872, 11727038, 51658256, 229044711, 1020550074, 4570049184, 20550100281, 92745397635, 420029964181, 1907917677098, 8690353843227, 39684067334191, 181626595148183, 833037353173956, 3828184693476046, 17623724932579910

Offset

0,3

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A296223 A045627 A007722 * A149009 A149010 A149011

Adjacent sequences: A149005 A149006 A149007 * A149009 A149010 A149011

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved