A200249 Number of 0..5 arrays x(0..n-1) of n elements with each no smaller than the sum of its previous elements modulo 6.

6, 21, 75, 267, 951, 3387, 12063, 42963, 153015, 544971, 1940943, 6912771, 24620199, 87686139, 312298815, 1112268723, 3961403799, 14108748843, 50249054127, 178964660067, 637392088455, 2270105585499, 8085100933407, 28795513971219

Offset

1,1

Comments

Column 5 of A200251.

Links

R. H. Hardin, Table of n, a(n) for n = 1..136

Formula

Empirical: a(n) = 3*a(n-1) +2*a(n-2).

Conjectures from Colin Barker, May 20 2018: (Start)

G.f.: 3*x*(2 + x) / (1 - 3*x - 2*x^2).

a(n) = (3*2^(-2-n)*((3-sqrt(17))^n*(-5+sqrt(17)) + (3+sqrt(17))^n*(5+sqrt(17)))) / sqrt(17).

(End)

Example

Some solutions for n=6:
..2....2....3....2....0....0....3....3....2....3....3....3....1....0....1....3
..5....4....5....5....1....3....3....4....5....4....4....4....1....0....1....3
..2....3....5....1....5....5....2....5....4....5....2....3....2....5....2....0
..5....3....1....2....2....4....4....5....5....1....5....5....4....5....5....2
..5....2....5....5....3....4....5....5....4....3....5....4....2....5....4....4
..3....4....5....4....5....5....5....5....5....4....2....4....4....3....5....5

Crossrefs

Cf. A200251.

Sequence in context: A107660 A200665 A200466 * A207097 A027281 A006814

Adjacent sequences: A200246 A200247 A200248 * A200250 A200251 A200252

Keyword

nonn

Author

R. H. Hardin, Nov 15 2011

Status

approved