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 A004538 #48 Apr 24 2024 05:26:31
%S A004538 -1,5,17,35,59,89,125,167,215,269,329,395,467,545,629,719,815,917,
%T A004538 1025,1139,1259,1385,1517,1655,1799,1949,2105,2267,2435,2609,2789,
%U A004538 2975,3167,3365,3569,3779,3995,4217,4445
%N A004538 a(n) = 3*n^2 + 3*n - 1.
%C A004538 Numbers k such that (4*k + 7)/3 is a square. - _Bruno Berselli_, Sep 11 2018
%H A004538 G. C. Greubel, <a href="/A004538/b004538.txt">Table of n, a(n) for n = 0..5000</a>
%H A004538 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A004538 From _Alexander Adamchuk_, Apr 12 2006: (Start)
%F A004538 a(n) = 5 * Sum_{k=1..n} k^4 / Sum_{k=1..n} k^2, n > 0.
%F A004538 a(n) = 5 * A000538(n) / A000330(n), n > 0. (End)
%F A004538 a(n) = a(n-1) + 6*n with a(0)=-1. - _Vincenzo Librandi_, Nov 18 2010
%F A004538 From _G. C. Greubel_, Sep 10 2018: (Start)
%F A004538 G.f.: (-1 + 8*x - x^2)/(1 - x)^3.
%F A004538 E.g.f.: (-1 + 6*x + 3*x^2)*exp(x). (End)
%F A004538 Sum_{n>=0} 1/a(n) = ( psi(1/2+sqrt(21)/6) - psi(1/2-sqrt(21)/6)) /sqrt(21) = -0.6286929... _R. J. Mathar_, Apr 24 2024
%t A004538 Table[5*Sum[k^4,{k,1,n}]/Sum[k^2,{k,1,n}], {n,1,20}] (* _Alexander Adamchuk_, Apr 12 2006 *)
%t A004538 Table[3n^2+3n-1,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{-1,5,17},40] (* _Harvey P. Dale_, Jan 18 2019 *)
%o A004538 (PARI) a(n)=3*n^2+3*n-1 \\ _Charles R Greathouse IV_, Jun 17 2017
%o A004538 (Magma) [3*n^2 + 3*n -1: n in [0..50]]; // _G. C. Greubel_, Sep 10 2018
%Y A004538 First differences of A033445.
%Y A004538 Cf. A028896, A003215, A077588, A000538, A000330.
%K A004538 sign,easy
%O A004538 0,2
%A A004538 _N. J. A. Sloane_, Eric T. Lane (ERICLANE(AT)UTCVM.UTC.EDU)