A149408 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), (0, 0, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 52, 192, 870, 3582, 16589, 71955, 338268, 1514672, 7199780, 32946510, 157849905, 733478937, 3534723692, 16611444982, 80413000420, 381184590682, 1851829209401, 8838170318225, 43060475311709, 206637959657937, 1009149879503074, 4864333089628588, 23802850312968338, 115160218352392668

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[i, 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: A149405 A149406 A149407 * A125529 A149409 A149410

Adjacent sequences: A149405 A149406 A149407 * A149409 A149410 A149411

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved