A058582 Expansion of (1+3*x+4*x^2)/(1-4*x^2+4*x^4).

1, 3, 8, 12, 28, 36, 80, 96, 208, 240, 512, 576, 1216, 1344, 2816, 3072, 6400, 6912, 14336, 15360, 31744, 33792, 69632, 73728, 151552, 159744, 327680, 344064, 704512, 737280, 1507328, 1572864, 3211264, 3342336, 6815744, 7077888

Offset: 0

Author

N. J. A. Sloane, Dec 26 2000

Keywords

• nonn
• easy

Comments

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]

Examples

			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
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 4, 0, -4).

Crossrefs

a(n)=T(n, 1), array T as in A064861.

Programs

Mathematica

f[k_] := 1 + Mod[k, 2]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 33}]
(* Clark Kimberling, Dec 29 2011 *)

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

Formula

a(n) = A032766(n+1)*A016116(n). - Philippe Deléham, Oct 11 2014