A148735 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, 0), (-1, 1, 1), (0, -1, 0), (1, 0, -1), (1, 0, 0)}.

1, 1, 3, 7, 25, 82, 304, 1137, 4419, 17624, 71591, 295945, 1242057, 5269407, 22632264, 98011100, 428245235, 1884755881, 8349296970, 37215394774, 166753657393, 750936303113, 3396894245330, 15429029717504, 70350785713817, 321889838514655, 1477642011814318, 6803673437466460, 31415097550714252

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A118398 A047974 A366593 * A148736 A148737 A148738

Adjacent sequences: A148732 A148733 A148734 * A148736 A148737 A148738

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved