A149495 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, 0, 1), (-1, 1, 1), (1, -1, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 14, 64, 263, 1264, 5641, 27604, 128072, 632378, 3000389, 14887097, 71618136, 356346004, 1730063109, 8622746137, 42130140402, 210201864844, 1031735210826, 5151197491389, 25369518303914, 126720652138666, 625708121062905, 3126353117696240, 15467971638524083, 77301685267909076

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A250399 A149494 A322206 * A137956 A357793 A341682

Adjacent sequences: A149492 A149493 A149494 * A149496 A149497 A149498

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved