A150346 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), (0, -1, 1), (0, 1, 0), (1, 1, 0)}.

1, 2, 7, 23, 90, 355, 1464, 6118, 26104, 113015, 493445, 2176366, 9662238, 43207699, 194076432, 876203269, 3971292756, 18066354458, 82435993765, 377251260801, 1730867213101, 7959519430017, 36678741055915, 169346773159360, 783265963408246, 3628518273182962, 16834332348922110, 78209778434661593

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[i, -1 + j, k, -1 + n] + aux[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: A150343 A150344 A150345 * A150347 A150348 A150349

Adjacent sequences: A150343 A150344 A150345 * A150347 A150348 A150349

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved