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A203233 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,2,3,2,3,2,...).

%I A203233 #13 May 04 2017 19:39:30
%S A203233 1,5,21,60,216,540,1836,4320,14256,32400,104976,233280,746496,1632960,
%T A203233 5178816,11197440,35271936,75582720,236825856,503884800,1572120576,
%U A203233 3325639680,10339716096,21767823360,67480252416,141490851840
%N A203233 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,2,3,2,3,2,...).
%H A203233 Robert Israel, <a href="/A203233/b203233.txt">Table of n, a(n) for n = 1..2559</a>
%F A203233 Conjecture: a(n)=12*a(n-2)-36*a(n-4) with G.f. x*(1+5*x+9*x^2) / (-1+6*x^2)^2 . - _R. J. Mathar_, Oct 15 2013, verified by _Robert Israel_, May 04 2017
%F A203233 a(n) = (5/12)*n*6^(n/2) if n is even, (5*n-1)*6^((n+1)/2)/24 if n is odd. - _Robert Israel_, May 04 2017
%p A203233 f:= proc(n) if n::even then (5/12)*n*6^(n/2) else (5*n-1)*6^((n+1)/2)/24 fi
%p A203233 end proc:
%p A203233 map(f, [$1..100]); # _Robert Israel_, May 04 2017
%t A203233 r = {3, 2, 3, 2, 3, 2};
%t A203233 s = Flatten[{r, r, r, r, r, r, r, r, r}];
%t A203233 t[n_] := Part[s, Range[n]]
%t A203233 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A203233 Table[a[n], {n, 1, 32}]     (* A203233 *)
%Y A203233 Cf. A203232, A212700 (bisection)
%K A203233 nonn
%O A203233 1,2
%A A203233 _Clark Kimberling_, Dec 30 2011