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 A028884 #78 Feb 05 2024 02:24:52
%S A028884 1,8,17,28,41,56,73,92,113,136,161,188,217,248,281,316,353,392,433,
%T A028884 476,521,568,617,668,721,776,833,892,953,1016,1081,1148,1217,1288,
%U A028884 1361,1436,1513,1592,1673,1756,1841,1928,2017,2108,2201,2296,2393
%N A028884 a(n) = (n + 3)^2 - 8.
%C A028884 From _Klaus Purath_, Jan 04 2023: (Start)
%C A028884 The product of two consecutive terms belongs to the sequence: a(n)*a(n+1) = a(a(n)+n) = (a(n)+n)*(a(n+1)-n-1) + 1.
%C A028884 a(n) is never divisible by primes given in A003629.
%C A028884 Each odd prime factor p divides exactly 2 out of any p consecutive terms. If a(i) and a(k) form such a pair that are divisible by p, then i + k == -6 (mod p).
%C A028884 The prime factors are listed in A038873 and the primes in A028886.
%C A028884 For n > 0, this is a proper subsequence of A079896.
%C A028884 Conjecture: a(n) = A079896(A265284(n-1)). -
%C A028884 (End)
%H A028884 Altug Alkan, <a href="/A028884/b028884.txt">Table of n, a(n) for n = 0..10000</a>
%H A028884 Patrick De Geest, <a href="http://www.worldofnumbers.com/consemor.htm">Palindromic Quasipronics of the form n(n+x)</a>.
%H A028884 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A028884 a(n) = a(n-1) + 2*n + 5 (with a(0) = 1). - _Vincenzo Librandi_, Aug 05 2010
%F A028884 a(n) = A028560(n) + 1; A014616(n) = floor(a(n+1)/4). - _Reinhard Zumkeller_, Apr 07 2013
%F A028884 G.f.: (-1 - 5*x + 4*x^2)/(x - 1)^3. - _R. J. Mathar_, Mar 24 2013
%F A028884 Sum_{n >= 0} 1/a(n) = 51/112 - Pi*cot(2*Pi*sqrt(2))/(4*sqrt(2)) = 1.3839174974448... . - _Vaclav Kotesovec_, Apr 10 2016
%F A028884 E.g.f.: (1 + 7*x + x^2)*exp(x). - _G. C. Greubel_, Aug 19 2017
%F A028884 Sum_{n >= 0} (-1)^n/a(n) = (-19 + 14*sqrt(2)*Pi*cosec(2*sqrt(2)*Pi))/112. - _Amiram Eldar_, Nov 04 2020
%F A028884 From _Klaus Purath_, Jan 04 2023: (Start)
%F A028884 a(n) = 2*a(n-1) - a(n-2) + 2, n >= 2.
%F A028884 a(n) = A082111(n) + n.
%F A028884 a(n) = A190576(n+1) - n. (End)
%F A028884 From _Amiram Eldar_, Feb 05 2024: (Start)
%F A028884 Product_{n>=1} (1 - 1/a(n)) = 7*Pi/(45*sqrt(2)*sin(2*sqrt(2)*Pi)).
%F A028884 Product_{n>=0} (1 + 1/a(n)) = (4*sqrt(14)/9)*sin(sqrt(7)*Pi)/sin(2*sqrt(2)*Pi). (End)
%e A028884 From _Stefano Spezia_, Nov 08 2022: (Start)
%e A028884 Illustrations for n = 0..4:
%e A028884 * * * * * * * * *
%e A028884 a(0) = 1 * * * *
%e A028884 * * * * * *
%e A028884 a(1) = 8 * *
%e A028884 * * * * *
%e A028884 a(2) = 17
%e A028884 .
%e A028884 * * * * * * * * * * * * * * * *
%e A028884 * * * *
%e A028884 * * * * * * * * *
%e A028884 * * * *
%e A028884 * * * * * * * * *
%e A028884 * * * *
%e A028884 * * * * * * * * * * * *
%e A028884 a(3) = 28 * *
%e A028884 * * * * * * * * *
%e A028884 a(4) = 41
%e A028884 (End)
%t A028884 Range[3, 50]^2 - 8 (* _Alonso del Arte_, Aug 15 2016 *)
%o A028884 (Haskell) a014616 n = (n * (n + 6) + 1) `div` 4 -- _Reinhard Zumkeller_, Apr 07 2013
%o A028884 (PARI) a(n)=(n+3)^2-8 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A028884 (Scala) (3 to 49).map(n => n * n - 8) // _Alonso del Arte_, May 07 2020
%Y A028884 Cf. A005563, A014616, A028560, A082111, A190576.
%K A028884 nonn,easy
%O A028884 0,2
%A A028884 _Patrick De Geest_
%E A028884 Definition corrected by _Omar E. Pol_, Jul 27 2009