A150782 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, 0), (1, 0, 0), (1, 1, -1), (1, 1, 1)}

1, 2, 8, 30, 134, 563, 2610, 11570, 54609, 249476, 1191209, 5545982, 26685261, 125844944, 608851334, 2898027333, 14078991088, 67481610993, 328888543542, 1584904306487, 7744255098228, 37479452647939, 183518303582422, 891252152124351, 4371628555676396, 21291573151253966, 104589772274521522

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, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, 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: A150779 A150780 A150781 * A150783 A150784 A150785

Adjacent sequences: A150779 A150780 A150781 * A150783 A150784 A150785

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved