A049658 a(n) = (F(8*n+5) - 2)/3, where F = A000045 (the Fibonacci sequence).

1, 77, 3648, 171409, 8052605, 378301056, 17772097057, 834910260653, 39223010153664, 1842646566961585, 86565165637040861, 4066720138373958912, 191049281337939028033, 8975249502744760358669

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..595
• Index entries for linear recurrences with constant coefficients, signature (48, -48, 1).

Crossrefs

Cf. A000045, A242671.

Programs

Magma

[(Fibonacci(8*n+5) - 2)/3: n in [0..30]]; // G. C. Greubel, Dec 02 2017

Mathematica

(Fibonacci[8Range[0,20]+5]-2)/3 (* or *) LinearRecurrence[{48,-48,1},{1,77,3648},20] (* Harvey P. Dale, Jun 20 2013 *)

PARI

for(n=0,30, print1((fibonacci(8*n+5) - 2)/3, ", ")) \\ G. C. Greubel, Dec 02 2017

Formula

G.f.: (1+29*x)/(1-48*x+48*x^2-x^3).

a(0)=1, a(1)=77, a(2)=3648, a(n) = 48*a(n-1)-48*a(n-2)+a(n-3). - Harvey P. Dale, Jun 20 2013

Product_{n>=1} (1 - 1/a(n)) = 3*(5+sqrt(5))/22 = (15/11) * A242671. - Amiram Eldar, Nov 28 2024

Extensions

Description corrected by and more terms from Michael Somos