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A203167 (n-1)-st elementary symmetric function of the first n terms of (2,2,1,2,2,1,2,2,1,...)=(A130196 for n>0).

%I A203167 #11 Feb 12 2018 21:05:15
%S A203167 1,4,8,20,48,64,144,320,384,832,1792,2048,4352,9216,10240,21504,45056,
%T A203167 49152,102400,212992,229376,475136,983040,1048576,2162688,4456448,
%U A203167 4718592,9699328,19922944,20971520,42991616,88080384,92274688,188743680
%N A203167 (n-1)-st elementary symmetric function of the first n terms of (2,2,1,2,2,1,2,2,1,...)=(A130196 for n>0).
%F A203167 From _R. J. Mathar_, Jul 02 2013: (Start)
%F A203167 Conjecture: a(n) = 8*a(n-3) - 16*a(n-6).
%F A203167 Conjecture: G.f.: x*(1+4*x+8*x^2+12*x^3+16*x^4) / (-1+4*x^3)^2.
%F A203167 (End)
%t A203167 f[k_] := 1 + Mod[k^2, 3]; t[n_] := Table[f[k], {k, 1, n}]
%t A203167 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A203167 Table[a[n], {n, 1, 33}]  (* A203167 *)
%Y A203167 Cf. A130196, A058582.
%K A203167 nonn
%O A203167 1,2
%A A203167 _Clark Kimberling_, Dec 30 2011