A073385 Eighth convolution of A000129(n+1) (generalized (2,1)-Fibonacci, called Pell numbers), n>=0, with itself.
1, 18, 189, 1500, 9945, 58014, 307197, 1507176, 6950295, 30443270, 127666539, 515754252, 2017069431, 7667214570, 28419251715, 102997948704, 365832349542, 1275914693196, 4376992440590
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (18,-135,528,-1044,504,1764,-2448,-1422,3308,1422, -2448,-1764,504,1044,528,135,18,1).
Programs
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Magma
R
:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1-2*x-x^2)^9 )); // G. C. Greubel, Oct 03 2022 -
Mathematica
CoefficientList[Series[1/(1-(2+x)x)^9,{x,0,20}],x] (* Harvey P. Dale, Apr 26 2017 *) -
Sage
taylor( 1/(1-2*x-x^2)^9, x, 0,27).list() # G. C. Greubel, Oct 03 2022
Formula
a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k)*binomial(n-k+8, 8)*binomial(n-k, k).
G.f.: 1/(1-(2+x)*x)^9.
a(n) = F''''''''(n+9, 2)/8!, that is, 1/8! times the 8th derivative of the (n+9)-th Fibonacci polynomial evaluated at x=2. - T. D. Noe, Jan 19 2006
Comments