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A028875 a(n) = n^2 - 5. 11

%I

%S -5,-4,-1,4,11,20,31,44,59,76,95,116,139,164,191,220,251,284,319,356,

%T 395,436,479,524,571,620,671,724,779,836,895,956,1019,1084,1151,1220,

%U 1291,1364,1439,1516,1595,1676,1759,1844,1931,2020,2111,2204,2299,2396

%N a(n) = n^2 - 5.

%C a(n) gives the values for a*c of indefinite binary quadratic forms [a, b, c] of discriminant D = 20 for b = 2*n. In general D = b^2 - 4*a*c > 0 and the form [a, b, c] is a*x^2 + b*x*y + c*y^2. - _Wolfdieter Lang_, Aug 15 2013

%C For n>2, a(n) represents the area of the triangle created by the three points defined with coordinates: (n-3,n-2), ((n-1)*n/2,n*(n+1)/2), and ((n+1)^2, (n+2)^2). - _J. M. Bergot_, May 22 2014

%H G. C. Greubel, <a href="/A028875/b028875.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Near-SquarePrime.html">Near-Square Prime</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F From _R. J. Mathar_, Apr 28 2008: (Start)

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

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

%F a(n) = 2*n + a(n-1) + 5, with n>0, a(0)=4. - _Vincenzo Librandi_, Aug 05 2010

%F a(-n) = a(n). - _Michael Somos_, May 26 2014

%F E.g.f.: (x^2 + x - 5)*exp(x). - _G. C. Greubel_, Aug 19 2017

%p A028875:=n->n^2-5; seq(A028875(n), n=0..100); # _Wesley Ivan Hurt_, Nov 13 2013

%t Range[0, 49]^2 - 5 (* _Alonso del Arte_, Aug 27 2013 *)

%o (Sage) [lucas_number2(2,n,2-n) for n in range(-1,49)] # _Zerinvary Lajos_, Mar 12 2009

%o (MAGMA) [n^2-5: n in [0..50]]; // _Wesley Ivan Hurt_, May 22 2014

%o (PARI) a(n)=n^2-5 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A028877 (subset of primes).

%K sign,easy

%O 0,1

%A _Patrick De Geest_, Dec 11 1999

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Last modified March 31 17:36 EDT 2020. Contains 333151 sequences. (Running on oeis4.)