A150362 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), (1, -1, 1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 23, 92, 359, 1519, 6276, 27364, 117440, 521307, 2285792, 10273806, 45763928, 207502571, 934410801, 4265733559, 19371739399, 88900966371, 406332773092, 1872782231503, 8604392647974, 39797648806791, 183621901037008, 851838827810155, 3944130822733590, 18343807527298937, 85186635277686814

Offset

0,2

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[-1 + i, j, k, -1 + n] + aux[-1 + 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: A150359 A150360 A150361 * A150363 A150364 A093636

Adjacent sequences: A150359 A150360 A150361 * A150363 A150364 A150365

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved