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A203150 (n-1)-st elementary symmetric function of the first n terms of (1,2,1,2,1,2,1,2,1,2,...)=A000034.

%I A203150 #25 Aug 12 2018 04:04:19
%S A203150 1,3,5,12,16,36,44,96,112,240,272,576,640,1344,1472,3072,3328,6912,
%T A203150 7424,15360,16384,33792,35840,73728,77824,159744,167936,344064,360448,
%U A203150 737280,770048,1572864,1638400,3342336,3473408,7077888,7340032
%N A203150 (n-1)-st elementary symmetric function of the first n terms of (1,2,1,2,1,2,1,2,1,2,...)=A000034.
%H A203150 Vincenzo Librandi, <a href="/A203150/b203150.txt">Table of n, a(n) for n = 1..1000</a>
%F A203150 Empirical G.f.: x*(1+3*x+x^2)/(1-4*x^2+4*x^4). - _Colin Barker_, Jan 03 2012
%F A203150 Conjecture: a(n) = (6*r*n+(1+3*(1-r)*n)*(1-(-1)^n))*r^(n-1)/8, where r=sqrt(2). - _Bruno Berselli_, Jan 03 2011
%e A203150 Let esf abbreviate "elementary symmetric function".  Then
%e A203150 0th esf of {1}:  1
%e A203150 1st esf of {1,2}:  1+2=3
%e A203150 2nd esf of {1,2,1} is 1*2+1*1+2*1=5
%t A203150 f[k_] := 1 + Mod[k + 1, 2];
%t A203150 t[n_] := Table[f[k], {k, 1, n}]
%t A203150 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A203150 Table[a[n], {n, 1, 33}]  (* A203150 *)
%Y A203150 Cf. A000034, A167667 (bisection?), A053220 (bisection?)
%K A203150 nonn,easy
%O A203150 1,2
%A A203150 _Clark Kimberling_, Dec 29 2011