A151010 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), (0, 1, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 39, 178, 840, 4007, 19340, 94128, 460168, 2259995, 11132979, 54970170, 271972002, 1347631186, 6685969540, 33205872514, 165056176495, 821039167010, 4086584248983, 20350736261471, 101389521255599, 505325574326270, 2519374282327881, 12564325986981825, 62675050088092712, 312713124134785503

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, -1 + j, 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A095939 A361358 A151009 * A151011 A151012 A151013

Adjacent sequences: A151007 A151008 A151009 * A151011 A151012 A151013

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved