A271494 Expansion of (1+16*x)/((1+4*x)*(1-8*x)).

1, 20, 112, 1088, 7936, 66560, 520192, 4210688, 33488896, 268697600, 2146435072, 17184063488, 137422176256, 1099578736640, 8795824586752, 70369817919488, 562945658454016, 4503616807239680, 36028728299487232, 288230651029618688, 2305841909702066176, 18446748471756062720

Offset: 0

Author

N. J. A. Sloane, Apr 15 2016

Keywords

• nonn
• easy

Comments

Sixth moments of the Rudin-Shapiro polynomials.

References

• Shalosh B. Ekhad, Explicit Generating Functions, Asymptotics, and More for the First 10 Even Moments of the Rudin-Shapiro Polynomials, Preprint, 2016.
• Doron Zeilberger, Personal Communication to N. J. A. Sloane, Apr 15 2016.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Christophe Doche, Even moments of generalized Rudin-Shapiro polynomials, Mathematics of computation 74.252 (2005): 1923-1935.
• Christophe Doche and Laurent Habsieger, Moments of the Rudin-Shapiro polynomials, Journal of Fourier Analysis and Applications 10.5 (2004): 497-505.
• Index entries for linear recurrences with constant coefficients, signature (4,32).

Crossrefs

Cf. A246036, A271495, A271496.

Programs

Mathematica

CoefficientList[Series[(1+16x)/((1+4x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{4,32},{1,20},30] (* Harvey P. Dale, May 13 2017 *)

PARI

Vec((1+16*x)/((1+4*x)*(1-8*x)) + O(x^50)) \\ Colin Barker, Apr 17 2016

Formula

From Colin Barker, Apr 17 2016: (Start)

a(n) = 2^(1+3*n)-(-4)^n.

a(n) = 4*a(n-1) + 32*a(n-2) for n>1.

(End)

a(n) = 4^n*A014551(n+1). - R. J. Mathar, Mar 08 2021