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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.

%I A200249 #10 May 20 2018 13:54:36
%S A200249 6,21,75,267,951,3387,12063,42963,153015,544971,1940943,6912771,
%T A200249 24620199,87686139,312298815,1112268723,3961403799,14108748843,
%U A200249 50249054127,178964660067,637392088455,2270105585499,8085100933407,28795513971219
%N 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.
%C A200249 Column 5 of A200251.
%H A200249 R. H. Hardin, <a href="/A200249/b200249.txt">Table of n, a(n) for n = 1..136</a>
%F A200249 Empirical: a(n) = 3*a(n-1) +2*a(n-2).
%F A200249 Conjectures from _Colin Barker_, May 20 2018: (Start)
%F A200249 G.f.: 3*x*(2 + x) / (1 - 3*x - 2*x^2).
%F A200249 a(n) = (3*2^(-2-n)*((3-sqrt(17))^n*(-5+sqrt(17)) + (3+sqrt(17))^n*(5+sqrt(17)))) / sqrt(17).
%F A200249 (End)
%e A200249 Some solutions for n=6:
%e A200249 ..2....2....3....2....0....0....3....3....2....3....3....3....1....0....1....3
%e A200249 ..5....4....5....5....1....3....3....4....5....4....4....4....1....0....1....3
%e A200249 ..2....3....5....1....5....5....2....5....4....5....2....3....2....5....2....0
%e A200249 ..5....3....1....2....2....4....4....5....5....1....5....5....4....5....5....2
%e A200249 ..5....2....5....5....3....4....5....5....4....3....5....4....2....5....4....4
%e A200249 ..3....4....5....4....5....5....5....5....5....4....2....4....4....3....5....5
%Y A200249 Cf. A200251.
%K A200249 nonn
%O A200249 1,1
%A A200249 _R. H. Hardin_, Nov 15 2011