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A103434
a(n) = Sum_{i=1..n} Fibonacci(2i)^2.
5
0, 1, 10, 74, 515, 3540, 24276, 166405, 1140574, 7817630, 53582855, 367262376, 2517253800, 17253514249, 118257345970, 810547907570, 5555578007051, 38078498141820, 260993908985724, 1788878864758285, 12261158144322310
OFFSET
0,3
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
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 *)
PROG
(Magma) [(1/5)*(Fibonacci(4*n+2)-2*n-1): n in [0..50]]; // Vincenzo Librandi, Apr 20 2011
CROSSREFS
Partial sums of A049684.
Bisection of A002571 and |A077916|.
Cf. A000045.
Sequence in context: A309884 A279284 A264082 * A119167 A233100 A266674
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Feb 08 2005
STATUS
approved