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A014283 a(n) = Fibonacci(n) - n^2. 2
0, 0, -3, -7, -13, -20, -28, -36, -43, -47, -45, -32, 0, 64, 181, 385, 731, 1308, 2260, 3820, 6365, 10505, 17227, 28128, 45792, 74400, 120717, 195689, 317027, 513388, 831140, 1345308, 2177285, 3523489, 5701731, 9226240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..280

Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1).

FORMULA

From Vladeta Jovovic, Jan 08 2002 : (Start)

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

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

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

MAPLE

with(combinat): seq((fibonacci(n)-n^2), n=0..40); # Zerinvary Lajos, Mar 21 2009

MATHEMATICA

Table[Fibonacci[n]-n^2, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, May 02 2011 *)

PROG

(MAGMA) [Fibonacci(n) - n^2: n in [0..40]]; // Vincenzo Librandi, May 03 2011

(PARI) vector(40, n, n--; fibonacci(n) - n^2) \\ G. C. Greubel, Jun 18 2019

(Sage) [fibonacci(n) - n^2 for n in (0..40)] # G. C. Greubel, Jun 18 2019

(GAP) List([0..50], n-> Fibonacci(n) - n^2) # G. C. Greubel, Jun 18 2019

CROSSREFS

Cf. A000045.

Sequence in context: A106080 A187819 A310266 * A294398 A033551 A022777

Adjacent sequences:  A014280 A014281 A014282 * A014284 A014285 A014286

KEYWORD

sign,changed

AUTHOR

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

STATUS

approved

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Last modified June 18 15:25 EDT 2019. Contains 324213 sequences. (Running on oeis4.)