A103434 - OEIS

%I #21 Sep 08 2022 08:45:16

%S 0,1,10,74,515,3540,24276,166405,1140574,7817630,53582855,367262376,

%T 2517253800,17253514249,118257345970,810547907570,5555578007051,

%U 38078498141820,260993908985724,1788878864758285,12261158144322310

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

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9, -16, 9, -1).

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

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

%F a(n) = Sum_{i=0..2n} (-1)^i*Fibonacci(i)*Fibonacci(i+1). - _Rigoberto Florez_, May 04 2019

%t Accumulate[Fibonacci[Range[0,40,2]]^2] (* _Harvey P. Dale_, Nov 14 2013 *)

%t LinearRecurrence[{9, -16, 9, -1},{0, 1, 10, 74},21] (* _Ray Chandler_, Sep 23 2015 *)

%o (Magma) [(1/5)*(Fibonacci(4*n+2)-2*n-1): n in [0..50]]; // _Vincenzo Librandi_, Apr 20 2011

%Y Partial sums of A049684.

%Y Bisection of A002571 and |A077916|.

%Y Cf. A000045.

%K nonn,easy

%O 0,3

%A _Ralf Stephan_, Feb 08 2005