A151053 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), (0, 0, -1), (0, 0, 1), (0, 1, 0), (1, 0, 0)}.

1, 3, 10, 37, 144, 586, 2454, 10491, 45670, 201428, 898710, 4047732, 18373856, 83991102, 386189282, 1785033011, 8288830692, 38645792022, 180849601258, 849093024414, 3998469899148, 18880505756862, 89373153794574, 424026472077136, 2015977545656546, 9603271271496564, 45828024248011082

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 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: A119244 A151052 A264231 * A151054 A052893 A052818

Adjacent sequences: A151050 A151051 A151052 * A151054 A151055 A151056

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved