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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A066706 A209003 A080022 * A057146 A344573 A300127

Adjacent sequences:  A192910 A192911 A192912 * A192914 A192915 A192916

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 12 2011

STATUS

approved

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Last modified October 17 00:35 EDT 2021. Contains 348048 sequences. (Running on oeis4.)