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

0,2

Comments

For a(n) in terms of U(n+1) and U(n) with U(n) = A000129(n+1) see the row polynomials of triangles A058402 and A058403 and the comment there.

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).

Formula

a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A000129(k+1) and c(k) = A073384(k).

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

Mathematica

CoefficientList[Series[1/(1-(2+x)x)^9, {x, 0, 20}], x] (* Harvey P. Dale, Apr 26 2017 *)

Prog

(Sage) taylor( 1/(1-2*x-x^2)^9, x, 0, 27).list() # G. C. Greubel, Oct 03 2022
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1-2*x-x^2)^9 )); // G. C. Greubel, Oct 03 2022

Crossrefs

Ninth (m=8) column of triangle A054456.

Cf. A000129, A058402, A058403, A073384.

Sequence in context: A288836 A341393 A023016 * A036219 A022646 A268447

Adjacent sequences: A073382 A073383 A073384 * A073386 A073387 A073388

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 02 2002

Status

approved