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%I #16 Oct 01 2023 12:45:00
%S 1,3,8,12,28,36,80,96,208,240,512,576,1216,1344,2816,3072,6400,6912,
%T 14336,15360,31744,33792,69632,73728,151552,159744,327680,344064,
%U 704512,737280,1507328,1572864,3211264,3342336,6815744,7077888
%N Expansion of (1+3*x+4*x^2)/(1-4*x^2+4*x^4).
%C Is a(n) the (n-1)-st elementary symmetric function of first n terms of (2,1,2,1,2,1,2,...)? See the Mathematica section. [_Clark Kimberling_, Dec 29 2011]
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 4, 0, -4).
%F a(n) = A032766(n+1)*A016116(n). - _Philippe Deléham_, Oct 11 2014
%e a(0) = 1*1 = 1, a(1) = 3*1 = 3, a(2) = 4*2 = 8, a(3) = 6*2 = 12, a(4) = 7*4 = 28, a(5) = 9*4 = 36, a(6) = 10*8 = 80, a(7) = 12*8 = 96, a(8) = 13*16 = 208, ... - _Philippe Deléham_, Oct 11 2014
%t f[k_] := 1 + Mod[k, 2]; t[n_] := Table[f[k], {k, 1, n}]
%t a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t Table[a[n], {n, 1, 33}]
%t (* _Clark Kimberling_, Dec 29 2011 *)
%o (PARI) Vec((1+3*x+4*x^2)/(1-4*x^2+4*x^4)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y a(n)=T(n, 1), array T as in A064861.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 26 2000
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