A103434 a(n) = Sum_{i=1..n} Fibonacci(2i)^2.

0, 1, 10, 74, 515, 3540, 24276, 166405, 1140574, 7817630, 53582855, 367262376, 2517253800, 17253514249, 118257345970, 810547907570, 5555578007051, 38078498141820, 260993908985724, 1788878864758285, 12261158144322310

Offset: 0

Author

Ralf Stephan, Feb 08 2005

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (9, -16, 9, -1).

Crossrefs

Partial sums of A049684.

Bisection of A002571 and |A077916|.

Cf. A000045.

Programs

Magma

[(1/5)*(Fibonacci(4*n+2)-2*n-1): n in [0..50]]; // Vincenzo Librandi, Apr 20 2011

Mathematica

Accumulate[Fibonacci[Range[0,40,2]]^2] (* Harvey P. Dale, Nov 14 2013 *)
LinearRecurrence[{9, -16, 9, -1},{0, 1, 10, 74},21] (* Ray Chandler, Sep 23 2015 *)

Formula

G.f.: x(1+x) / ((1-7x+x^2)(1-x)^2).

a(n) = (1/5)*(Fibonacci(4n+2) - 2n - 1).

a(n) = Sum_{i=0..2n} (-1)^i*Fibonacci(i)*Fibonacci(i+1). - Rigoberto Florez, May 04 2019