A049677 a(n) = (F(8*n+6) + F(8*n+1))/3, where F = A000045 (the Fibonacci sequence).

3, 137, 6436, 302355, 14204249, 667297348, 31348771107, 1472724944681, 69186723628900, 3250303285613619, 152695067700211193, 7173417878624312452, 336997945227642474051, 15831730007820571967945, 743754312422339240019364, 34940620953842123708942163, 1641465430518157475080262297

Offset

0,1

Links

Indranil Ghosh, Table of n, a(n) for n = 0..596

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (47,-1).

Formula

From Philippe Deléham, Nov 18 2008: (Start)

a(n) = 47*a(n-1) - a(n-2), a(0)=3, a(1)=137.

G.f.: (3-4*x)/(1-47*x+x^2). (End)

Example

a(2) = (F(8 * 2 + 6) + F(8 * 2 + 1)) / 3 = (F(22) + F(17)) / 3 = (17711 + 1597) / 3 = 19308 / 3 = 6436. - Indranil Ghosh, Feb 05 2017

Mathematica

Table[(Fibonacci[8*n+6] + Fibonacci[8*n+1])/3, {n, 0, 30}] (* or *) LinearRecurrence[{47, -1}, {3, 137}, 30] (* G. C. Greubel, Dec 02 2017 *)

Prog

(PARI) a(n) = (fibonacci(8*n+6)+fibonacci(8*n+1))/3; \\ Michel Marcus, Feb 05 2017
(Magma) [(Fibonacci(8*n+6) + Fibonacci(8*n+1))/3: n in [0..30]]; // G. C. Greubel, Dec 02 2017

Crossrefs

Cf. A000045, A049676, A049678, A049679.

Sequence in context: A082923 A336202 A231904 * A030247 A139956 A236193

Adjacent sequences: A049674 A049675 A049676 * A049678 A049679 A049680

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved