A150237 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), (-1, 0, 0), (0, 0, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 6, 22, 83, 319, 1290, 5347, 22406, 95151, 410219, 1784533, 7813236, 34466618, 153083361, 683137112, 3061675811, 13783972184, 62292859805, 282377271190, 1283902635103, 5854575259529, 26762246203248, 122603995307273, 562895787156388, 2589502394769981, 11933432303823800, 55085204063079946

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A150235 A150236 A068946 * A122449 A150238 A150239

Adjacent sequences: A150234 A150235 A150236 * A150238 A150239 A150240

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved