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 A028878 #56 Feb 05 2024 02:23:07
%S A028878 3,10,19,30,43,58,75,94,115,138,163,190,219,250,283,318,355,394,435,
%T A028878 478,523,570,619,670,723,778,835,894,955,1018,1083,1150,1219,1290,
%U A028878 1363,1438,1515,1594,1675,1758,1843,1930,2019,2110,2203,2298,2395
%N A028878 a(n) = (n+3)^2 - 6.
%C A028878 a(n-3) = n^2 - 6, n>=0, with a(-3) = -6, a(-2) = -5, a(-1) = -2 gives the values for a*c of indefinite binary quadratic forms [a, b, c] of discriminant D = 24 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 16 2013
%H A028878 G. C. Greubel, <a href="/A028878/b028878.txt">Table of n, a(n) for n = 0..1000</a>
%H A028878 Patrick De Geest, <a href="http://www.worldofnumbers.com/consemor.htm">Palindromic Quasipronics of the form n(n+x)</a>.
%H A028878 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A028878 a(n) = a(n-1) + 2*n + 5 (with a(0)=3). - _Vincenzo Librandi_, Aug 05 2010
%F A028878 From _Bruno Berselli_, Sep 02 2011: (Start)
%F A028878 G.f.: (x+1)*(3-2*x)/(1-x)^3.
%F A028878 a(n) = a(-n-6).
%F A028878 a(n) mod (n+1) = n-1. (End)
%F A028878 a(n) = A000290(n+3) - 6. - _Omar E. Pol_, Dec 12 2012
%F A028878 E.g.f.: (x^2 + 7*x + 3)*exp(x). - _G. C. Greubel_, Aug 19 2017
%F A028878 From _Amiram Eldar_, Nov 04 2020: (Start)
%F A028878 Sum_{n>=0} 1/a(n) = (47 - 5*sqrt(6)*Pi*cot(sqrt(6)*Pi))/60.
%F A028878 Sum_{n>=0} (-1)^n/a(n) = (-23 + 5*sqrt(6)*Pi*cosec(sqrt(6)*Pi))/60. (End)
%F A028878 From _Amiram Eldar_, Feb 05 2024: (Start)
%F A028878 Product_{n>=0} (1 - 1/a(n)) = (5*sqrt(2/21)/3)*sin(sqrt(7)*Pi)/sin(sqrt(6)*Pi).
%F A028878 Product_{n>=0} (1 + 1/a(n)) = sqrt(15/2)*sin(sqrt(5)*Pi)/sin(sqrt(6)*Pi). (End)
%p A028878 A028878:=n->(n+3)^2-6: seq(A028878(n), n=0..100); # _Wesley Ivan Hurt_, Apr 28 2017
%t A028878 Table[(n + 3)^2 - 6, {n,0,50}] (* _G. C. Greubel_, Aug 19 2017 *)
%o A028878 (PARI) a(n)=(n+3)^2-6 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A028878 Cf. A000290.
%K A028878 nonn,easy
%O A028878 0,1
%A A028878 _Patrick De Geest_
%E A028878 Definition corrected by _Omar E. Pol_, Jul 27 2009