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 A153169 #30 Jun 04 2025 11:30:32
%S A153169 19,43,75,115,163,219,283,355,435,523,619,723,835,955,1083,1219,1363,
%T A153169 1515,1675,1843,2019,2203,2395,2595,2803,3019,3243,3475,3715,3963,
%U A153169 4219,4483,4755,5035,5323,5619,5923,6235,6555,6883,7219,7563,7915,8275,8643,9019,9403
%N A153169 a(n) = 4*n^2 + 12*n + 3.
%C A153169 Sequence gives values of x such that x^3 + 6*x^2 = y^2 since a(n)^3 + 6*a(n)^2 = (8*n^3 + 36*n^2 + 42*n + 9)^2.
%C A153169 The complete list of nonnegative values of x in x^3 + 6*x^2 = y^2 is given by A028878. - _Bruno Berselli_, Jan 25 2012
%H A153169 Vincenzo Librandi, <a href="/A153169/b153169.txt">Table of n, a(n) for n = 1..1000</a>
%H A153169 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A153169 From _Colin Barker_, Jan 24 2012: (Start)
%F A153169 G.f.: x*(19 - 14*x + 3*x^2)/(1-x)^3.
%F A153169 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=19, a(2)=43, a(3)=75. (End)
%F A153169 Sum_{n>=1} 1/a(n) = -2/15 + tan(sqrt(3/2)*Pi)*Pi/(4*sqrt(6)). - _Amiram Eldar_, Mar 02 2023
%F A153169 From _Elmo R. Oliveira_, Jun 03 2025: (Start)
%F A153169 E.g.f.: -3 + (3 + 16*x + 4*x^2)*exp(x).
%F A153169 a(n) = A028878(2*n) for n >= 1. (End)
%t A153169 LinearRecurrence[{3, -3, 1}, {19, 43, 75}, 50] (* _Vincenzo Librandi_, Feb 25 2012 *)
%o A153169 (Magma) I:=[19, 43, 75]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Feb 25 2012
%o A153169 (PARI) for(n=1, 50, print1(4*n^2 + 12*n + 3", ")); \\ _Vincenzo Librandi_, Feb 25 2012
%Y A153169 Cf. A028878, A153167.
%K A153169 nonn,easy
%O A153169 1,1
%A A153169 _Vincenzo Librandi_, Dec 20 2008
%E A153169 Definition rewritten by _Bruno Berselli_, Jan 25 2012