A150284 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, 1, 1), (0, 1, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 6, 23, 91, 365, 1529, 6552, 28329, 123993, 548439, 2441621, 10936491, 49261695, 222834197, 1011830689, 4610728789, 21071941581, 96554920713, 443512797674, 2041601345727, 9416130159996, 43506635862108, 201349038433485, 933234334342715, 4331475468258564, 20129858878208957, 93661790304961226

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A220899 A150282 A150283 * A150285 A150286 A150287

Adjacent sequences: A150281 A150282 A150283 * A150285 A150286 A150287

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved