A150694 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, 1, 1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 26, 118, 438, 2080, 8216, 39830, 163110, 799424, 3352272, 16535140, 70515690, 349211512, 1508207086, 7488678448, 32664348338, 162479694960, 714384839432, 3558016315308, 15747177498792, 78501167165856, 349366389355596, 1742799416394194, 7793186299312930, 38895607137774622, 174645356756872834

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A150691 A150692 A150693 * A150695 A150696 A150697

Adjacent sequences: A150691 A150692 A150693 * A150695 A150696 A150697

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved