A096140 a(n) = sum of n Fibonacci numbers starting from F(n).

0, 1, 3, 10, 29, 81, 220, 589, 1563, 4126, 10857, 28513, 74792, 196041, 513619, 1345282, 3522981, 9224881, 24153636, 63239221, 165569195, 433476726, 1134874513, 2971168705, 7778667024, 20364889681, 53316094755, 139583544634

Offset: 0

Author

Amarnath Murthy, Jul 16 2004

Keywords

• nonn
• easy
• changed

Examples

			a(4)= F(4) + F(5) + F(6) + F(7) = 3 + 5 + 8 + 13 = 29.
x + 3*x^2 + 10*x^3 + 29*x^4 + 81*x^5 + 220*x^6 + 589*x^7 + ...
		

Crossrefs

Cf. A005013.

Programs

PARI

a(n)=sum(k=n,2*n-1,fibonacci(k))

Formula

a(n) = Fibonacci(2*n+1)-Fibonacci(n+1). - Vladeta Jovovic, Jul 17 2004

G.f.: x*(1-x+x^2)/((1-3*x+x^2)*(1-x-x^2)). a(n)=F(2n+1)-F(n+1). - Mario Catalani (mario.catalani(AT)unito.it), Jul 19 2004

Binomial transform of A005013. - Michael Somos, Apr 13 2012

Extensions

Extended by Ray Chandler, Jul 17 2004

a(0)=0 by Michael Somos, Apr 13 2012