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A014283 a(n) = Fibonacci(n) - n^2. 2

%I

%S 0,0,-3,-7,-13,-20,-28,-36,-43,-47,-45,-32,0,64,181,385,731,1308,2260,

%T 3820,6365,10505,17227,28128,45792,74400,120717,195689,317027,513388,

%U 831140,1345308,2177285,3523489,5701731,9226240

%N a(n) = Fibonacci(n) - n^2.

%H Vincenzo Librandi, <a href="/A014283/b014283.txt">Table of n, a(n) for n = 0..280</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,1,2,-1).

%F From _Vladeta Jovovic_, Jan 08 2002 : (Start)

%F a(n) = ((1+sqrt(5))^n - (1-sqrt(5))^n)/(2^n*sqrt(5)) - n^2.

%F a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5).

%F G.f.: (-3*x^2 + 5*x^3)/(1 - 4*x + 5*x^2 - x^3 - 2*x^4 + x^5). (End)

%p with(combinat): seq((fibonacci(n)-n^2), n=0..40); # _Zerinvary Lajos_, Mar 21 2009

%t Table[Fibonacci[n]-n^2,{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, May 02 2011 *)

%o (MAGMA) [Fibonacci(n) - n^2: n in [0..40]]; // _Vincenzo Librandi_, May 03 2011

%o (PARI) vector(40, n, n--; fibonacci(n) - n^2) \\ _G. C. Greubel_, Jun 18 2019

%o (Sage) [fibonacci(n) - n^2 for n in (0..40)] # _G. C. Greubel_, Jun 18 2019

%o (GAP) List([0..50], n-> Fibonacci(n) - n^2) # _G. C. Greubel_, Jun 18 2019

%Y Cf. A000045.

%K sign

%O 0,3

%A fink(AT)cadvision.com (A. R. Fink)

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Last modified July 19 08:33 EDT 2019. Contains 325155 sequences. (Running on oeis4.)