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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

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

FORMULA

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

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

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|.

Sequence in context: A044578 A279284 A264082 * A119167 A233100 A266674

Adjacent sequences:  A103431 A103432 A103433 * A103435 A103436 A103437

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Feb 08 2005

STATUS

approved

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Last modified October 20 19:40 EDT 2018. Contains 316401 sequences. (Running on oeis4.)