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A203235 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (1,1,1,3,1,1,1,3,...).

%I A203235 #7 Oct 15 2013 14:19:37
%S A203235 1,2,3,10,13,16,19,60,69,78,87,270,297,324,351,1080,1161,1242,1323,
%T A203235 4050,4293,4536,4779,14580,15309,16038,16767,51030,53217,55404,57591,
%U A203235 174960,181521,188082,194643,590490,610173,629856,649539,1968300
%N A203235 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (1,1,1,3,1,1,1,3,...).
%F A203235 Conjecture: a(n) = 6*a(n-4)-9*a(n-8) with G.f. x*(1+2*x+3*x^2+10*x^3+7*x^4+4*x^5+x^6) / ( (-1+3*x^4)^2 ). - _R. J. Mathar_, Oct 15 2013
%t A203235 r = {1, 1, 1, 3, 1, 1, 1, 3};
%t A203235 s = Flatten[{r, r, r, r, r, r, r, r, r}];
%t A203235 t[n_] := Part[s, Range[n]]
%t A203235 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A203235 Table[a[n], {n, 1, 47}]     (* A203235 *)
%Y A203235 Cf. A203234.
%K A203235 nonn
%O A203235 1,2
%A A203235 _Clark Kimberling_, Dec 30 2011