A192912 Coefficient of x in the reduction by (x^3 -> x + 1) of the polynomial F(n+1)*x^n, where F(n)=A000045 (Fibonacci sequence).

0, 1, 0, 3, 10, 24, 78, 231, 680, 2035, 6052, 18000, 53590, 159471, 474580, 1412397, 4203304, 12509144, 37227624, 110790405, 329715412, 981242533, 2920205614, 8690615136, 25863518300, 76970566973, 229066599960, 681708726543

Offset

0,4

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*(1-x-x^2+2*x^3)/(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, 1, 0, 3, 10, 24}, 28] (* Ray Chandler, Aug 02 2015 *)

Prog

(PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1-x-x^2+2*x^3)/(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] cat Coefficients(R!( x*(1-x-x^2+2*x^3)/(1-x-4*x^2-5*x^3-2*x^4+x^5-x^6) )); // G. C. Greubel, Jan 12 2019
(Sage) (x*(1-x-x^2+2*x^3)/(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, 1, 0, 3, 10, 24];; 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: A293797 A179608 A340686 * A168062 A176952 A212068

Adjacent sequences: A192909 A192910 A192911 * A192913 A192914 A192915

Keyword

nonn

Author

Clark Kimberling, Jul 12 2011

Status

approved