A149050 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), (0, 1, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 3, 10, 39, 149, 621, 2608, 11362, 50005, 224087, 1013844, 4634939, 21348758, 99021584, 461872495, 2165291885, 10194743118, 48184538956, 228506836782, 1086931778012, 5184096470608, 24785574274311, 118761815637600, 570191410379617, 2742543994332775, 13213240012589938, 63757133657178463

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, k, -1 + n] + aux[i, -1 + j, -1 + 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: A111749 A149048 A149049 * A300974 A149051 A151064

Adjacent sequences: A149047 A149048 A149049 * A149051 A149052 A149053

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved