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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). 1

%I #11 Feb 12 2018 21:05:15

%S 1,4,8,20,48,64,144,320,384,832,1792,2048,4352,9216,10240,21504,45056,

%T 49152,102400,212992,229376,475136,983040,1048576,2162688,4456448,

%U 4718592,9699328,19922944,20971520,42991616,88080384,92274688,188743680

%N (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 From _R. J. Mathar_, Jul 02 2013: (Start)

%F Conjecture: a(n) = 8*a(n-3) - 16*a(n-6).

%F Conjecture: G.f.: x*(1+4*x+8*x^2+12*x^3+16*x^4) / (-1+4*x^3)^2.

%F (End)

%t f[k_] := 1 + Mod[k^2, 3]; t[n_] := Table[f[k], {k, 1, n}]

%t a[n_] := SymmetricPolynomial[n - 1, t[n]]

%t Table[a[n], {n, 1, 33}] (* A203167 *)

%Y Cf. A130196, A058582.

%K nonn

%O 1,2

%A _Clark Kimberling_, Dec 30 2011

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)