A165206 a(n) = (3-4*n)*F(2*n-2) + (4-7*n)*F(2*n-1).

1, -3, -25, -112, -416, -1411, -4537, -14085, -42653, -126794, -371554, -1076423, -3089555, -8799207, -24897121, -70052356, -196151492, -546916555, -1519249933, -4206274089, -11611243109, -31967026718, -87796880710

Offset: 0

Author

Paul Barry, Sep 07 2009

Keywords

• easy
• sign

Comments

Hankel transform of A165205.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1).

Crossrefs

Cf. A000045.

Programs

GAP

F:=Fibonacci;; List([0..30], n-> (3-4*n)*F(2*n-2)+(4-7*n)*F(2*n-1) ); # G. C. Greubel, Jul 18 2019

Magma

F:=Fibonacci; [(3-4*n)*F(2*n-2)+(4-7*n)*F(2*n-1): n in [0..30]]; // G. C. Greubel, Jul 18 2019

Mathematica

Table[(3-4n)Fibonacci[2n-2]+(4-7n)Fibonacci[2n-1],{n,0,30}] (* or *) LinearRecurrence[{6,-11,6,-1},{1,-3,-25,-112},30] (* Harvey P. Dale, Aug 25 2013 *)

PARI

vector(30, n, n--; f=fibonacci; (3-4*n)*f(2*n-2)+(4-7*n)*f(2*n-1)) \\ G. C. Greubel, Jul 18 2019

Sage

f=fibonacci; [(3-4*n)*f(2*n-2)+(4-7*n)*f(2*n-1) for n in (0..30)] # G. C. Greubel, Jul 18 2019

Formula

G.f.: (1-9*x+4*x^2-x^3)/(1-3*x+x^2)^2 = (1-x)/(1-3*x+x^2) - 5*x/(1-3*x+x^2)^2.

a(n) = -5*A001871(n-1) + A001519(n+1). - R. J. Mathar, Dec 16 2024