A073397 Eighth convolution of A002605(n) (generalized (2,2)-Fibonacci), n>=0, with itself.

1, 18, 198, 1680, 12060, 76824, 446952, 2420352, 12363120, 60151520, 280833696, 1265442048, 5528697408, 23507763840, 97575960960, 396398370816, 1579498956288, 6184543546368, 23833455191040

Offset

0,2

Comments

For a(n) in terms of U(n+1) and U(n), with U(n) = A002605(n), see A073387 and the row polynomials of triangles A073405 and A073406.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (18,-126,384,-144,-2016,3360,4608,-12384,-8512, 24768,18432,-26880,-32256,4608,24576,16128,4608,512).

Formula

a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A002605(k) and c(k) = A073394(k).

a(n) = Sum_{k=0..floor(n/2)} (binomial(n-k+8, 8)*binomial(n-k, k)*2^(n-k).

G.f.: 1/(1-2*x*(1+x))^9.

Mathematica

CoefficientList[Series[1/(1-2*x-2*x^2)^9, {x, 0, 30}], x] (* G. C. Greubel, Oct 06 2022 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-2*x-2*x^2)^9 )); // G. C. Greubel, Oct 06 2022
(SageMath)
def A073397_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-2*x-2*x^2)^9 ).list()
A073397_list(30) # G. C. Greubel, Oct 06 2022

Crossrefs

Ninth (m=8) column of triangle A073387.

Cf. A002605, A073387, A073394, A073405, A073406.

Sequence in context: A264356 A034727 A060532 * A020920 A083812 A086573

Adjacent sequences: A073394 A073395 A073396 * A073398 A073399 A073400

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 02 2002

Status

approved