A200249 - OEIS

%I #10 May 20 2018 13:54:36

%S 6,21,75,267,951,3387,12063,42963,153015,544971,1940943,6912771,

%T 24620199,87686139,312298815,1112268723,3961403799,14108748843,

%U 50249054127,178964660067,637392088455,2270105585499,8085100933407,28795513971219

%N 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.

%C Column 5 of A200251.

%H R. H. Hardin, <a href="/A200249/b200249.txt">Table of n, a(n) for n = 1..136</a>

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

%F Conjectures from _Colin Barker_, May 20 2018: (Start)

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

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

%F (End)

%e Some solutions for n=6:

%e ..2....2....3....2....0....0....3....3....2....3....3....3....1....0....1....3

%e ..5....4....5....5....1....3....3....4....5....4....4....4....1....0....1....3

%e ..2....3....5....1....5....5....2....5....4....5....2....3....2....5....2....0

%e ..5....3....1....2....2....4....4....5....5....1....5....5....4....5....5....2

%e ..5....2....5....5....3....4....5....5....4....3....5....4....2....5....4....4

%e ..3....4....5....4....5....5....5....5....5....4....2....4....4....3....5....5

%Y Cf. A200251.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 15 2011