A190173 a(n) = Sum_{1 <= i < j <= n} F(i)*F(j), where F(k) is the k-th Fibonacci number.

0, 1, 5, 17, 52, 148, 408, 1101, 2937, 7777, 20504, 53912, 141520, 371113, 972573, 2547825, 6672876, 17473996, 45754280, 119797205, 313650865, 821177281, 2149916400, 5628629232, 14736064032, 38579712913, 101003317493, 264430632401, 692289215332, 1812438042052

Offset: 1

Author

Emeric Deutsch, May 31 2011

Keywords

• nonn
• easy

Examples

			a(4) = F(1)*F(2) + F(1)*F(3) + F(1)*F(4) + F(2)*F(3) + F(2)*F(4) + F(3)*F(4) = 1 + 2 + 3 + 2 + 3 + 6 = 17.
		

Links

• Vincenzo Librandi and Bruno Berselli, Table of n, a(n) for n = 1..1000 (First 211 terms from Vincenzo Librandi)
• Index entries for linear recurrences with constant coefficients, signature (4,-2,-6,4,2,-1).

Crossrefs

Cf. A000045.

Programs

Magma

[Fibonacci(n+1)^2 - Fibonacci(n+2) + (1-(-1)^n)/2: n in [1..30]]; // Vincenzo Librandi, Jun 05 2011

Maple

with(combinat): seq(fibonacci(n+1)^2-fibonacci(n+2)+1/2-(1/2)*(-1)^n, n = 1 .. 30);

Mathematica

Table[Fibonacci[n + 1]^2 - Fibonacci[n + 1] + (1 - (-1)^n)/2, {n,1,50}] (* G. C. Greubel, Mar 04 2017 *)

PARI

a(n)=fibonacci(n+1)^2-fibonacci(n+2)+n%2 \\ Charles R Greathouse IV, Jun 08 2011

Formula

a(n) = F(n+1)^2 - F(n+2) + (1-(-1)^n)/2.

G.f.: x^2*(1+x-x^2)/((1-x)*(1+x)*(1-x-x^2)*(1-3*x+x^2)). - Bruno Berselli, Jun 20 2012