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 A152813 #60 Oct 18 2024 19:39:01
%S A152813 3,15,31,51,75,103,135,171,211,255,303,355,411,471,535,603,675,751,
%T A152813 831,915,1003,1095,1191,1291,1395,1503,1615,1731,1851,1975,2103,2235,
%U A152813 2371,2511,2655,2803,2955,3111,3271,3435,3603,3775,3951,4131,4315,4503,4695
%N A152813 a(n) = 2*n^2 + 10*n + 3.
%C A152813 Nonzero x values at solutions of Diophantine equation 2*x^3 + 19*x^2 = y^2.
%C A152813 Nonnegative integers m such that 2*m + 19 is a square. - _Vincenzo Librandi_, Mar 01 2013
%H A152813 Vincenzo Librandi, <a href="/A152813/b152813.txt">Table of n, a(n) for n = 0..1000</a>
%H A152813 Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
%H A152813 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A152813 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 22 2012
%F A152813 G.f.: (3 + 6*x - 5*x^2)/(1 -x)^3. - _Vincenzo Librandi_, Jan 04 2013
%F A152813 a(n-1) = 2*n^2 + 2*n - 9. - _Avi Friedlich_, Mar 27 2015
%F A152813 a(n) = A001844(n+2) - 10. - _Robert Israel_, Mar 27 2015
%F A152813 Sum_{n>=0} 1/a(n) = 14/45 + tan(sqrt(19)*Pi/2)*Pi/(2*sqrt(19)). - _Amiram Eldar_, Mar 02 2023
%F A152813 E.g.f.: (3 + 12*x + 2*x^2)*exp(x). - _Elmo R. Oliveira_, Oct 18 2024
%t A152813 LinearRecurrence[{3, -3, 1}, {3, 15, 31}, 50] (* _Vincenzo Librandi_, Feb 22 2012 *)
%t A152813 CoefficientList[Series[(3 + 6*x - 5*x^2)/(1 - x)^3, {x, 0, 60}], x] (* _Vincenzo Librandi_, Jan 04 2013 *)
%o A152813 (Magma) I:=[3, 15, 31]; [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 A152813 (PARI) for(n=0, 40, print1(2*n^2+10*n+3", ")); \\ _Vincenzo Librandi_, Feb 22 2012
%Y A152813 Cf. A001844.
%K A152813 nonn,easy
%O A152813 0,1
%A A152813 _Vincenzo Librandi_, Dec 17 2008
%E A152813 Edited and extended by _Jon E. Schoenfield_, Jun 17 2010