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 A154590 #29 Jun 04 2025 11:07:14
%S A154590 24,46,72,102,136,174,216,262,312,366,424,486,552,622,696,774,856,942,
%T A154590 1032,1126,1224,1326,1432,1542,1656,1774,1896,2022,2152,2286,2424,
%U A154590 2566,2712,2862,3016,3174,3336,3502,3672,3846,4024,4206,4392,4582,4776,4974,5176
%N A154590 a(n) = 2*n^2 + 16*n + 6.
%C A154590 Eighth diagonal of A144562.
%C A154590 2*a(n) + 52 is a square.
%H A154590 Harvey P. Dale, <a href="/A154590/b154590.txt">Table of n, a(n) for n = 1..1000</a>
%H A154590 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A154590 a(n) = 2*A116711(n+3).
%F A154590 G.f.: -2*x*(3*x-4)*(x-3)/(x-1)^3.
%F A154590 From _Amiram Eldar_, Mar 02 2023: (Start)
%F A154590 Sum_{n>=1} 1/a(n) = 35/468 - cot(sqrt(13)*Pi)*Pi/(4*sqrt(13)).
%F A154590 Sum_{n>=1} (-1)^(n+1)/a(n) = 121/468 + cosec(sqrt(13)*Pi)*Pi/(4*sqrt(13)). (End)
%F A154590 From _Elmo R. Oliveira_, Jun 04 2025: (Start)
%F A154590 E.g.f.: 2*(exp(x)*(x^2 + 9*x + 3) - 3).
%F A154590 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t A154590 Table[2n^2+16n+6,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{24,46,72},50] (* _Harvey P. Dale_, Dec 27 2011 *)
%o A154590 (PARI) a(n)=2*n^2+16*n+6 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A154590 Cf. A067076, A116711, A144562, A153238.
%K A154590 nonn,easy,less
%O A154590 1,1
%A A154590 _Vincenzo Librandi_, Jan 12 2009
%E A154590 Corrected (a(31) added) by _Harvey P. Dale_, Dec 27 2011