A149013 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), (1, 0, -1), (1, 1, -1)}.

1, 1, 3, 9, 35, 116, 500, 1860, 8288, 33222, 151006, 634144, 2927959, 12686672, 59289782, 262829326, 1239619599, 5592148566, 26562347627, 121489768762, 580326142766, 2683779258274, 12878825133211, 60098900650217, 289507169955153, 1361099053157427, 6577911281816518, 31119637635957412

Offset

0,3

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, 1 + 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: A067787 A332370 A130491 * A149014 A149015 A151452

Adjacent sequences: A149010 A149011 A149012 * A149014 A149015 A149016

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved