A151095 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), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 1, -1)}.

1, 3, 11, 43, 179, 771, 3411, 15371, 70283, 324971, 1516195, 7125731, 33691907, 160107627, 764108987, 3660048235, 17586950003, 84740141795, 409295012819, 1981116681227, 9607426955019, 46670258489995, 227056918475331, 1106181623926499, 5395847682861859, 26350328313268011, 128814007312154683

Offset

0,2

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A151094 A339043 A103821 * A219262 A196151 A149071

Adjacent sequences: A151092 A151093 A151094 * A151096 A151097 A151098

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved