A151183 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, 1, -1), (1, 0, 0), (1, 1, 0), (1, 1, 1)}

1, 3, 12, 51, 225, 1026, 4726, 22114, 104174, 494451, 2359312, 11304641, 54375383, 262284928, 1268589445, 6149011950, 29863315708, 145281743211, 707832694711, 3453344196471, 16868125168892, 82483885309055, 403737004717802, 1977966198960109, 9698342043716415, 47588764638443821, 233676780351372292

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[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: A007854 A151182 A151316 * A180898 A110167 A151317

Adjacent sequences: A151180 A151181 A151182 * A151184 A151185 A151186

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved