A148558 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, 0, 0), (0, -1, 1), (0, 1, 0), (1, -1, 0)}.

1, 1, 3, 6, 18, 47, 151, 444, 1474, 4751, 15980, 54263, 188405, 654422, 2326335, 8306683, 29854080, 108664545, 397687346, 1460169528, 5417588114, 20172041308, 75314119276, 283455950368, 1069878059090, 4046382347316, 15403955808207, 58772144664246, 224605482392280, 862987851193742, 3321884504024162

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A148555 A148556 A148557 * A148559 A108507 A287212

Adjacent sequences: A148555 A148556 A148557 * A148559 A148560 A148561

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved