A150303 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, -1, 1), (-1, 1, 0), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 21, 82, 282, 1198, 4466, 19705, 76858, 347131, 1397815, 6429031, 26498484, 123329949, 517100523, 2429332648, 10327174912, 48879963250, 210096616126, 1000125434896, 4337820817891, 20749634479045, 90690386324898, 435549017087419, 1916054338405430, 9232861896129354, 40845399173564374

Offset

0,2

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A150300 A150301 A150302 * A150304 A150305 A150306

Adjacent sequences: A150300 A150301 A150302 * A150304 A150305 A150306

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved