A148326 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), (0, -1, 0), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 5, 14, 42, 127, 406, 1384, 4674, 16231, 57908, 207172, 759480, 2799649, 10388278, 39267427, 148491557, 566578382, 2183452049, 8421213079, 32796434160, 128237720641, 502717621685, 1986380784640, 7859822136004, 31232721688184, 124731244842505, 498653956893148, 2003101284597936

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, -1 + k, -1 + n] + aux[i, 1 + j, 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: A025274 A132833 A293347 * A148327 A092493 A316779

Adjacent sequences: A148323 A148324 A148325 * A148327 A148328 A148329

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved