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A049677 a(n) = (F(8*n+6) + F(8*n+1))/3, where F=A000045 (the Fibonacci sequence). 1
3, 137, 6436, 302355, 14204249, 667297348, 31348771107, 1472724944681, 69186723628900, 3250303285613619, 152695067700211193, 7173417878624312452, 336997945227642474051, 15831730007820571967945, 743754312422339240019364, 34940620953842123708942163, 1641465430518157475080262297 (list; graph; refs; listen; history; text; internal format)
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. A049676, A049678, A049679.

Sequence in context: A037120 A082923 A231904 * A030247 A139956 A236193

Adjacent sequences:  A049674 A049675 A049676 * A049678 A049679 A049680

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified September 22 19:01 EDT 2018. Contains 315270 sequences. (Running on oeis4.)