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A203234 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (1,1,1,2,1,1,1,2,...).

%I A203234 #7 Oct 15 2013 14:13:14
%S A203234 1,2,3,7,9,11,13,28,32,36,40,84,92,100,108,224,240,256,272,560,592,
%T A203234 624,656,1344,1408,1472,1536,3136,3264,3392,3520,7168,7424,7680,7936,
%U A203234 16128,16640,17152,17664,35840,36864,37888,38912,78848,80896
%N A203234 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (1,1,1,2,1,1,1,2,...).
%F A203234 Conjecture: a(n) = 4*a(n-4)-4*a(n-8) with G.f. x*(1+2*x+3*x^2+7*x^3+5*x^4+3*x^5+x^6) / (-1+2*x^4)^2 . - _R. J. Mathar_, Oct 15 2013
%t A203234 r = {1, 1, 1, 2, 1, 1, 1, 2};
%t A203234 s = Flatten[{r, r, r, r, r, r, r, r, r}];
%t A203234 t[n_] := Part[s, Range[n]]
%t A203234 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A203234 Table[a[n], {n, 1, 45}]     (* A203234 *)
%Y A203234 Cf. A203235.
%K A203234 nonn
%O A203234 1,2
%A A203234 _Clark Kimberling_, Dec 30 2011