A049654 a(n) = (F(8*n+1) - 1)/3 where F=A000045 (the Fibonacci sequence).

0, 11, 532, 25008, 1174859, 55193380, 2592914016, 121811765387, 5722560059188, 268838511016464, 12629687457714635, 593326472001571396, 27873714496616140992, 1309471254868957055243, 61517275264344365455444

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, A156093.

Programs

Magma

[(Fibonacci(8*n+1) - 1)/3: n in [0..30]]; // G. C. Greubel, Dec 02 2017

Mathematica

LinearRecurrence[{48, -48, 1}, {0, 11, 532}, 50] (* or *) Table[( Fibonacci[8*n+1]-1)/3, {n,0,30}] (* G. C. Greubel, Dec 02 2017 *)
CoefficientList[Series[-x(11+4x)/((x-1)(x^2-47*x+1)),{x,0,14}],x] (* Stefano Spezia, Feb 18 2024 *)

PARI

for(n=0,30, print1((fibonacci(8*n+1) - 1)/3, ", ")) \\ G. C. Greubel, Dec 02 2017

Formula

From R. J. Mathar, Oct 26 2015: (Start)

G.f.: -x*(11+4*x) / ( (x-1)*(x^2-47*x+1) ).

a(n) = 11*|A156093(n)|+4*|A156093(n-1)|. (End)