A149357 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, 0, 1), (0, -1, 1), (0, 0, -1), (1, 1, 0)}.

1, 1, 4, 12, 43, 163, 631, 2525, 10321, 42811, 180088, 765880, 3286441, 14215607, 61902944, 271139438, 1193813735, 5280214067, 23449724862, 104524431296, 467440584451, 2096715316321, 9430597111447, 42522968296897, 192180053280261, 870389180724247, 3949764095984244, 17956474896695226

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, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A220881 A149355 A149356 * A149358 A149359 A259223

Adjacent sequences: A149354 A149355 A149356 * A149358 A149359 A149360

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved