A049676 a(n) = (F(8*n+3) + F(8*n+1))/3, where F = A000045 (the Fibonacci sequence).

1, 41, 1926, 90481, 4250681, 199691526, 9381251041, 440719107401, 20704416796806, 972666870342481, 45694638489299801, 2146675342126748166, 100848046441467864001, 4737711507406862859881, 222571592801681086550406, 10456127150171604205009201

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Examples

			a(2) = (F(8 * 2 + 3) + F(8 * 2 + 1)) / 3 = (F(19) + F(17)) / 3 = (4181 + 1597) / 3 = 5778 / 3 = 1926. - _Indranil Ghosh_, Feb 04 2017
		

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).

Crossrefs

Cf. A000045.

Programs

Magma

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

Mathematica

Table[(Fibonacci[8*n + 3] + Fibonacci[8*n + 1])/3, {n, 0, 20}] (* Wesley Ivan Hurt, Feb 04 2017 *)
LinearRecurrence[{47,-1}, {1,41}, 30] (* G. C. Greubel, Dec 02 2017 *)

PARI

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

Formula

From Philippe Deléham, Nov 18 2008: (Start)

a(n) = 47*a(n-1) - a(n-2), a(0)=1, a(1)=41.

G.f.: (1-6*x)/(1-47*x+x^2). (End)

Extensions

More terms from Indranil Ghosh, Feb 04 2017