A150454 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, -1, 0), (0, 1, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 7, 25, 95, 384, 1559, 6606, 28013, 121326, 528787, 2323865, 10305291, 45842790, 205583679, 924004141, 4176135747, 18927081330, 86065623587, 392613070741, 1794642375921, 8228016991562, 37783626445495, 173921566304244, 801849368774407, 3703338607359942, 17131714254509809, 79355150543712787

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, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A242728 A116396 A150453 * A150455 A150456 A150457

Adjacent sequences: A150451 A150452 A150453 * A150455 A150456 A150457

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved