A151237 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, 0, 0), (0, -1, 0), (0, 1, 0), (1, 1, 0), (1, 1, 1)}.

1, 3, 14, 63, 298, 1428, 6906, 33653, 164836, 810060, 3993446, 19727978, 97630392, 483860652, 2400763156, 11923446689, 59266186460, 294785399216, 1467099385086, 7305154655534, 36390338352432, 181345090767820, 903997336345772, 4507679568564746, 22482713911686816, 112160886877865048

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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[i, -1 + j, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A320499 A091701 A242637 * A151238 A026243 A058139

Adjacent sequences: A151234 A151235 A151236 * A151238 A151239 A151240

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved