A148738 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, 1), (-1, 1, 0), (0, -1, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 7, 25, 84, 323, 1263, 5170, 21691, 93163, 407255, 1807711, 8124917, 36903800, 169163090, 781396520, 3633981175, 16999571547, 79933706284, 377570306382, 1790673354481, 8523043486189, 40697695158038, 194894404202650, 935750984180599, 4503450820637610, 21720021050852564, 104959537188008910

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A148735 A148736 A148737 * A148739 A129084 A287892

Adjacent sequences: A148735 A148736 A148737 * A148739 A148740 A148741

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved