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%I #10 Oct 31 2013 12:17:28
%S 0,1,4,16,56,188,608,1920,5952,18192,54976,164608,489088,1443776,
%T 4238336,12382208,36022272,104407296,301618176,868765696,2495715328,
%U 7152286720,20452548608,58369409024,166276481024,472876388352
%N Number of 1's that appear among all ternary strings of length n that contain no consecutive 1's.
%D Ralph P. Grimaldi, Ternary Strings with No Consecutive 1's, Ars Combin. 89 (2008), 321-343.
%F (sqrt(3)/18)*((1+sqrt(3))^n - (1-sqrt(3))^n)+(n/12)*((1+sqrt(3))^(n+1)+(1-sqrt(3))^(n+1))
%F Conjecture: a(n)=A073388(n-1). [From _R. J. Mathar_, Aug 18 2008]
%t f[n_] := Simplify[(2Sqrt[3] (-(1 - Sqrt[3])^n + (1 + Sqrt[3])^n) + 3n*((1 - Sqrt[3])^(1 + n) + (1 + Sqrt[3])^(1 + n)))/36]; Table[ f[n], {n, 0, 25}] (* _Robert G. Wilson v_ *)
%K nonn
%O 0,3
%A Ralph P. Grimaldi (ralph.grimaldi(AT)rose-hulman.edu), Aug 03 2005
%E More terms from _Robert G. Wilson v_, Aug 05 2005