A151047 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, 0, 1), (0, 1, 0), (1, 0, 0)}.

1, 3, 10, 35, 132, 524, 2145, 8924, 37693, 161604, 701218, 3068181, 13515463, 59931900, 267372422, 1198695390, 5395604431, 24377747242, 110533789419, 502767066982, 2293016680176, 10483543994331, 48042092202958, 220635526540888, 1015233950976577, 4679668922908784, 21606351450045311

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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A151046 A221130 A084781 * A008984 A151048 A149038

Adjacent sequences: A151044 A151045 A151046 * A151048 A151049 A151050

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved