A150480 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, 0, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 25, 100, 398, 1662, 6976, 29977, 129475, 566816, 2493202, 11062201, 49284182, 220890452, 993482996, 4488000583, 20334399427, 92443775146, 421325198097, 1925424389461, 8818025397164, 40473844104805, 186116185552614, 857426204220226, 3956486404788201, 18285520844677554, 84628687328684228

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, -1 + k, -1 + n] + aux[i, 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: A074421 A150478 A150479 * A150481 A150482 A150483

Adjacent sequences: A150477 A150478 A150479 * A150481 A150482 A150483

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved