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, 90522348871680, 339263015528448, 1255995653197824, 4597442198728704

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