A073383 Sixth convolution of A000129(n+1) (generalized (2,1)-Fibonacci, called Pell numbers), n>=0, with itself.

1, 14, 119, 784, 4396, 22008, 101220, 435696, 1777986, 6943244, 26129950, 95282992, 338108876, 1171554776, 3975215844, 13239402960, 43364985867, 139925413866, 445409413421, 1400429394784, 4353771487912

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (14,-77,196,-161,-238,427,184,-427,-238,161,196,77, 14,1).

Formula

a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A000129(k+1) and c(k) = A073382(k).

a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(n-k+6, 6) * binomial(n-k, k).

a(n) = (7*(173205 +212028*n +96812*n^2 +20728*n^3 +2092*n^4 +80*n^5)*(n+1)* U(n+1) + (262125 +435150*n +232364*n^2 +54548*n^3 +5836*n^4 +232*n^5)*(n+2)* U(n) )/(6!*8^4), with U(n) = A000129(n+1), n >= 0.

G.f.: 1/(1-(2+x)*x)^7.

a(n) = F''''''(n+7, 2)/6!, that is, 1/6! times the 6th derivative of the (n+7)-th Fibonacci polynomial evaluated at x=2. - T. D. Noe, Jan 19 2006

Mathematica

CoefficientList[Series[1/(1-2*x-x^2)^7, {x, 0, 70}], x] (* G. C. Greubel, Oct 02 2022 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1-2*x-x^2)^7 )); // G. C. Greubel, Oct 02 2022
(SageMath)
def A073383_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-2*x-x^2)^7 ).list()
A073383_list(40) # G. C. Greubel, Oct 02 2022

Crossrefs

Seventh (m=6) column of triangle A054456, A073382.

Cf. A000129.

Sequence in context: A284766 A341390 A023012 * A022642 A268446 A221230

Adjacent sequences: A073380 A073381 A073382 * A073384 A073385 A073386

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 02 2002

Status

approved