A049657 a(n) = (F(8*n+3) - 2)/3, where F = A000045 (the Fibonacci sequence).

0, 29, 1393, 65472, 3075821, 144498145, 6788337024, 318907342013, 14981856737617, 703828359326016, 33064951031585165, 1553348870125176769, 72974331944851723008, 3428240252537905804637, 161054317537336721094961

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

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, A344212.

Programs

Magma

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

Mathematica

LinearRecurrence[{48, -48, 1}, {0, 29, 1393}, 50] (* or *) Table[( Fibonacci[8*n+3] - 2)/3, {n,0,30}] (* G. C. Greubel, Dec 02 2017 *)

PARI

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

Formula

G.f.: -x*(29+x) / ( (x-1)*(x^2-47*x+1) ).

Product_{n>=1} (1 - 1/a(n)) = 2*(1+1/sqrt(5))/3 = (2/3) * A344212. - Amiram Eldar, Nov 28 2024

Extensions

Description corrected by and more terms from Michael Somos