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 A154591 #29 May 27 2024 16:18:09
%S A154591 27,51,79,111,147,187,231,279,331,387,447,511,579,651,727,807,891,979,
%T A154591 1071,1167,1267,1371,1479,1591,1707,1827,1951,2079,2211,2347,2487,
%U A154591 2631,2779,2931,3087,3247,3411,3579,3751,3927,4107,4291,4479,4671,4867,5067,5271
%N A154591 a(n) = 2*n^2 + 18*n + 7.
%C A154591 Ninth diagonal of A144562.
%C A154591 2*a(n) + 67 is a square.
%H A154591 Vincenzo Librandi, <a href="/A154591/b154591.txt">Table of n, a(n) for n = 1..1000</a>
%H A154591 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A154591 G.f.: (9*x^2-6*x-7)/(x-1)^3. - _Bruno Berselli_, Dec 07 2011
%F A154591 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 22 2012
%F A154591 Sum_{n>=1} 1/a(n) = 1621/20097 + tan(sqrt(67)*Pi/2)*Pi/(2*sqrt(67)). - _Amiram Eldar_, Feb 25 2023
%F A154591 E.g.f.: (7 + 20*x + 2*x^2)*exp(x). - _G. C. Greubel_, May 27 2024
%t A154591 LinearRecurrence[{3, -3, 1}, {27, 51, 79}, 50] (* _Vincenzo Librandi_, Feb 22 2012 *)
%o A154591 (Magma) I:=[27, 51, 79]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 22 2012
%o A154591 (PARI) for(n=1, 40, print1(2*n^2 + 18*n + 7", ")); \\ _Vincenzo Librandi_, Feb 22 2012
%o A154591 (SageMath) [2*n^2+18*n+7 for n in range(1,51)] # _G. C. Greubel_, May 27 2024
%Y A154591 Cf. A067076, A144562, A153238.
%K A154591 nonn,easy
%O A154591 1,1
%A A154591 _Vincenzo Librandi_, Jan 12 2009