A150506 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, 0, 1), (1, 0, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 25, 102, 414, 1805, 7815, 35323, 158644, 733072, 3369245, 15799972, 73770858, 349586259, 1650776523, 7883670078, 37542772998, 180365623658, 864515802872, 4172921778396, 20104175611203, 97408657759242, 471235087095606, 2290330542518136, 11117532170213077, 54174311113381971, 263709713662432669

Offset

0,2

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, 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: A150503 A150504 A150505 * A150507 A150508 A150509

Adjacent sequences: A150503 A150504 A150505 * A150507 A150508 A150509

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved