This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A028875 #72 Feb 16 2025 08:32:35
%S A028875 -5,-4,-1,4,11,20,31,44,59,76,95,116,139,164,191,220,251,284,319,356,
%T A028875 395,436,479,524,571,620,671,724,779,836,895,956,1019,1084,1151,1220,
%U A028875 1291,1364,1439,1516,1595,1676,1759,1844,1931,2020,2111,2204,2299,2396
%N A028875 a(n) = n^2 - 5.
%C A028875 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 A028875 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 A028875 G. C. Greubel, <a href="/A028875/b028875.txt">Table of n, a(n) for n = 0..1000</a>
%H A028875 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Near-SquarePrime.html">Near-Square Prime</a>.
%H A028875 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A028875 From _R. J. Mathar_, Apr 28 2008: (Start)
%F A028875 G.f.: x^3*(4 - x - x^2)/(1-x)^3.
%F A028875 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A028875 a(n) = 2*n + a(n-1) + 5, with n>0, a(0)=4. - _Vincenzo Librandi_, Aug 05 2010
%F A028875 a(-n) = a(n). - _Michael Somos_, May 26 2014
%F A028875 E.g.f.: (x^2 + x - 5)*exp(x). - _G. C. Greubel_, Aug 19 2017
%F A028875 From _Amiram Eldar_, Nov 04 2020: (Start)
%F A028875 Sum_{n>=0} 1/a(n) = -(1 + sqrt(5)*Pi*cot(sqrt(5)*Pi))/10.
%F A028875 Sum_{n>=0} (-1)^n/a(n) = -(1 + sqrt(5)*Pi*cosec(sqrt(5)*Pi))/10. (End)
%F A028875 From _Amiram Eldar_, Feb 05 2024: (Start)
%F A028875 Product_{n>=0} (1 - 1/a(n)) = sqrt(6/5)*sin(sqrt(6)*Pi)/sin(sqrt(5)*Pi).
%F A028875 Product_{n>=3} (1 + 1/a(n)) = sqrt(5)*Pi/(6*sin(sqrt(5)*Pi)). (End)
%p A028875 A028875:=n->n^2-5; seq(A028875(n), n=0..100); # _Wesley Ivan Hurt_, Nov 13 2013
%t A028875 Range[0, 49]^2 - 5 (* _Alonso del Arte_, Aug 27 2013 *)
%o A028875 (Magma) [n^2-5: n in [0..50]]; // _Wesley Ivan Hurt_, May 22 2014
%o A028875 (PARI) a(n)=n^2-5 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A028875 Cf. A028877 (subset of primes).
%K A028875 sign,easy
%O A028875 0,1
%A A028875 _Patrick De Geest_, Dec 11 1999