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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A286209 A293797 A179608 * A168062 A176952 A212068

Adjacent sequences:  A192909 A192910 A192911 * A192913 A192914 A192915

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 12 2011

STATUS

approved

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Last modified May 23 05:03 EDT 2019. Contains 323508 sequences. (Running on oeis4.)