A149417 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, 1, 1), (1, 0, -1), (1, 0, 1), (1, 1, -1)}

1, 1, 4, 12, 54, 203, 913, 3791, 17421, 76369, 357010, 1610906, 7618852, 35049764, 167219609, 780154851, 3746904339, 17660665005, 85252847312, 405012623438, 1962958881010, 9384294780340, 45630045874621, 219250204141161, 1068911354389637, 5157484620366595, 25199960350383735, 122013300433826613

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A053454 A149415 A149416 * A151478 A125528 A124005

Adjacent sequences: A149414 A149415 A149416 * A149418 A149419 A149420

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved