A150136 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), (0, 0, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 20, 72, 278, 1115, 4621, 19636, 84959, 373712, 1664116, 7493105, 34046132, 155922456, 718990578, 3335141541, 15552372406, 72859635607, 342751911710, 1618370036557, 7666976762013, 36431523233690, 173586679447721, 829155017445644, 3969551383992211, 19043725820723301, 91536357017160498

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, k, -1 + n] + aux[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: A059279 A154381 A150135 * A195186 A150137 A150138

Adjacent sequences: A150133 A150134 A150135 * A150137 A150138 A150139

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved