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 A028881 #64 Feb 05 2024 02:24:31
%S A028881 2,9,18,29,42,57,74,93,114,137,162,189,218,249,282,317,354,393,434,
%T A028881 477,522,569,618,669,722,777,834,893,954,1017,1082,1149,1218,1289,
%U A028881 1362,1437,1514,1593,1674,1757,1842,1929,2018,2109,2202,2297,2394
%N A028881 a(n) = n^2 - 7.
%C A028881 a(n), n>=0, with a(0) = -7, a(1) = -6 and a(2) = -3, gives the values for a*c of indefinite binary quadratic forms [a, b, c] of discriminant D = 28 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
%C A028881 The product of two consecutive terms belongs to the sequence. - _Klaus Purath_, Dec 13 2022 [a(n)*a(n+1) = a(n^2 + n - 7). - _Wolfdieter Lang_, Dec 15 2022]
%H A028881 G. C. Greubel, <a href="/A028881/b028881.txt">Table of n, a(n) for n = 3..1000</a>
%H A028881 Patrick De Geest, <a href="http://www.worldofnumbers.com/consemor.htm">Palindromic Quasipronics of the form n(n+x)</a>
%H A028881 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A028881 a(n) = a(n-1) + 2*n - 1, with a(3)=2. - _Vincenzo Librandi_, Aug 05 2010
%F A028881 G.f.: x^3*(2+3*x-3*x^2)/(1-x)^3. - _Colin Barker_, Feb 17 2012
%F A028881 E.g.f.: (1/2)*(2*(x^2 + x -7)*exp(x) + 14 + 12*x + 3*x^2). - _G. C. Greubel_, Aug 19 2017
%F A028881 From _Amiram Eldar_, Nov 04 2020: (Start)
%F A028881 Sum_{n>=3} 1/a(n) = (8 - sqrt(7)*Pi*cot(sqrt(7)*Pi))/14.
%F A028881 Sum_{n>=3} (-1)^(n+1)/a(n) = (-10 + 3*sqrt(7)*Pi*cosec(sqrt(7)*Pi))/42. (End)
%F A028881 From _Amiram Eldar_, Feb 05 2024: (Start)
%F A028881 Product_{n>=3} (1 - 1/a(n)) = (9/(4*sqrt(14)))*sin(2*sqrt(2)*Pi)/sin(sqrt(7)*Pi).
%F A028881 Product_{n>=3} (1 + 1/a(n)) = (3*sqrt(21/2)/5)*sin(sqrt(6)*Pi)/sin(sqrt(7)*Pi). (End)
%t A028881 LinearRecurrence[{3,-3,1}, {2,9,18}, 50] (* _G. C. Greubel_, Aug 19 2017 *)
%o A028881 (PARI) a(n)=n^2-7 \\ _Charles R Greathouse IV_, Oct 07 2015
%K A028881 nonn,easy
%O A028881 3,1
%A A028881 _Patrick De Geest_