A150522 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, 0), (-1, 1, 1), (0, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 25, 103, 438, 1906, 8534, 38910, 178973, 831918, 3903555, 18424142, 87390499, 416636868, 1994523916, 9577325284, 46124889133, 222762556911, 1078206910781, 5228740616624, 25404695312998, 123636141233037, 602534246383341, 2940309095447973, 14366156409233040, 70267513702574711

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A150519 A150520 A150521 * A150523 A150524 A150525

Adjacent sequences: A150519 A150520 A150521 * A150523 A150524 A150525

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved