A148518 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, 1), (-1, 1, 0), (1, -1, -1), (1, 0, 0)}.

1, 1, 3, 5, 17, 38, 143, 373, 1466, 4154, 16828, 50791, 210707, 666064, 2807184, 9189830, 39240386, 132194457, 570286809, 1966064255, 8552315969, 30060812789, 131683741780, 470526690791, 2073321169224, 7513385707338, 33274711381632, 122070988898003, 542994124029664, 2013558558341355

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A148515 A148516 A148517 * A077796 A241249 A067062

Adjacent sequences: A148515 A148516 A148517 * A148519 A148520 A148521

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved