A151101 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, 1, -1), (0, 1, 1), (1, 0, 0)}.

1, 3, 11, 43, 183, 797, 3574, 16223, 74919, 348413, 1636926, 7728125, 36735049, 175206264, 839653986, 4034201277, 19450853963, 93965830417, 455155856199, 2208144191025, 10734880227452, 52253712398104, 254775237149807, 1243519514802906, 6077610959396950, 29730078108932190, 145593549939873856

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, -1 + k, -1 + n] + aux[i, -1 + 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: A049158 A151100 A063031 * A151102 A151103 A049189

Adjacent sequences: A151098 A151099 A151100 * A151102 A151103 A151104

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved