A192913 Coefficient of x^2 in the reduction by (x^3 -> x + 1) of the polynomial F(n+1)*x^n, where F(n)=A000045 (Fibonacci sequence).

0, 0, 2, 3, 10, 32, 91, 273, 816, 2420, 7209, 21456, 63842, 190008, 565470, 1682835, 5008192, 14904512, 44356229, 132005445, 392851940, 1169138532, 3479389655, 10354762656, 30816068600, 91709498068, 272930078466, 812247687927

Offset

0,3

Comments

(See A192911.)

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,4,5,2,-1,1).

Formula

(See A192911.)

G.f.: x^2*(1+x)*(2-x) / (1 - x - 4*x^2 - 5*x^3 - 2*x^4 + x^5 - x^6). - R. J. Mathar, May 08 2014

Example

(See A192911.)

Mathematica

(See A192911.)
LinearRecurrence[{1, 4, 5, 2, -1, 1}, {0, 0, 2, 3, 10, 32}, 28] (* Ray Chandler, Aug 02 2015 *)

Prog

(PARI) my(x='x+O('x^30)); concat([0, 0], Vec(x^2*(1+x)*(2-x)/(1-x-4*x^2 -5*x^3-2*x^4+x^5-x^6))) \\ G. C. Greubel, Jan 12 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0, 0] cat Coefficients(R!( x^2*(1+x)*(2-x)/(1-x-4*x^2-5*x^3-2*x^4+x^5-x^6) )); // G. C. Greubel, Jan 12 2019
(Sage) (x^2*(1+x)*(2-x)/(1-x-4*x^2-5*x^3-2*x^4+x^5-x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 12 2019
(GAP) a:=[0, 0, 2, 3, 10, 32];; for n in [7..30] do a[n]:=a[n-1]+4*a[n-2] +5*a[n-3]+2*a[n-4]-a[n-5]+a[n-6]; od; a; # G. C. Greubel, Jan 12 2019

Crossrefs

Cf. A192232, A192744, A192911.

Sequence in context: A353052 A209003 A080022 * A364208 A358895 A057146

Adjacent sequences: A192910 A192911 A192912 * A192914 A192915 A192916

Keyword

nonn

Author

Clark Kimberling, Jul 12 2011

Status

approved