A150493 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, 0, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 7, 25, 101, 400, 1687, 7130, 30801, 134130, 591179, 2618893, 11699353, 52508678, 236771609, 1072349619, 4874373833, 22221592336, 101625788493, 465924405515, 2140863919623, 9859201392294, 45490213019045, 210244716359400, 973372017677157, 4513073364973540, 20952996698952751, 97410376431605323

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, 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: A346814 A178118 A150492 * A150494 A150495 A150496

Adjacent sequences: A150490 A150491 A150492 * A150494 A150495 A150496

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved