A149676 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, 0), (-1, 0, 1), (0, 0, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 17, 65, 263, 1099, 4611, 19819, 86035, 376603, 1662343, 7388127, 33010177, 148236927, 668470943, 3026007299, 13743999351, 62608319811, 285986666109, 1309560779337, 6009771380813, 27636815645785, 127330865243225, 587657881935223, 2716533517201397, 12576248494088001, 58302458370749869

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, 1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A092896 A149674 A149675 * A149677 A273856 A012765

Adjacent sequences: A149673 A149674 A149675 * A149677 A149678 A149679

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved