A148067 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, -1, 0), (-1, 1, -1), (-1, 1, 1), (1, 0, 0)}.

1, 1, 2, 3, 12, 25, 87, 189, 788, 1893, 7569, 18601, 80506, 207493, 874156, 2280579, 10100264, 27140517, 117684741, 318421209, 1430927370, 3951930221, 17460909038, 48431305459, 219878196682, 619212387825, 2771909420147, 7828026283149, 35809758410988, 102329069152021, 462524102337463, 1324171950218941

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[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] + 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: A148064 A148065 A148066 * A148068 A148069 A148070

Adjacent sequences: A148064 A148065 A148066 * A148068 A148069 A148070

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved