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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
OFFSET
0,3
COMMENTS
(See A192911.)
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 12 2011
STATUS
approved