A148845 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, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 28, 85, 315, 1055, 4012, 13985, 54082, 193919, 757327, 2767218, 10875615, 40282189, 159004452, 594976144, 2355738462, 8884815803, 35256788279, 133810866365, 531868815609, 2028932703003, 8074680435556, 30932776387067, 123224123759839, 473724053938601, 1888553495309558

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, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A260961 A230822 A332727 * A148846 A163062 A148847

Adjacent sequences: A148842 A148843 A148844 * A148846 A148847 A148848

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved