A148756 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, 1), (1, -1, 0), (1, 0, 1)}

1, 1, 3, 7, 28, 77, 328, 1032, 4561, 15405, 69863, 247581, 1139957, 4191007, 19505310, 73723498, 345996567, 1336688246, 6313660360, 24830303768, 117888042833, 470535221695, 2243426487708, 9066875262306, 43381843668078, 177214005001044, 850444498221412, 3506406506099757, 16870406935037750

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, j, -1 + 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] + 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: A148753 A148754 A148755 * A352701 A351771 A148757

Adjacent sequences: A148753 A148754 A148755 * A148757 A148758 A148759

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved