A149283 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, 0), (-1, 0, 1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 11, 44, 146, 642, 2239, 10080, 37666, 171218, 663592, 3053331, 12116439, 56196754, 227206025, 1059367428, 4350268844, 20366889356, 84658346439, 397770494430, 1669447188227, 7866672042155, 33291883541903, 157236375815510, 670231722511354, 3171728208270064, 13602768720471067

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A149280 A149281 A149282 * A151436 A149284 A149285

Adjacent sequences: A149280 A149281 A149282 * A149284 A149285 A149286

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved