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 A154600 #27 May 30 2024 06:57:10
%S A154600 33,61,93,129,169,213,261,313,369,429,493,561,633,709,789,873,961,
%T A154600 1053,1149,1249,1353,1461,1573,1689,1809,1933,2061,2193,2329,2469,
%U A154600 2613,2761,2913,3069,3229,3393,3561,3733,3909,4089,4273,4461,4653,4849,5049,5253
%N A154600 a(n) = 2*n^2 + 22*n + 9.
%C A154600 Eleventh diagonal of A144562.
%C A154600 2*a(n) + 103 is a square.
%H A154600 Vincenzo Librandi, <a href="/A154600/b154600.txt">Table of n, a(n) for n = 1..1000</a>
%H A154600 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A154600 From _Vincenzo Librandi_, Feb 26 2012: (Start)
%F A154600 G.f: x*(33 - 38*x + 9*x^2)/(1-x)^3.
%F A154600 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A154600 Sum_{n>=1} 1/a(n) = 257162/3084939 + tan(sqrt(103)*Pi/2)*Pi/(2*sqrt(103)). - _Amiram Eldar_, Feb 25 2023
%F A154600 E.g.f.: -9 + (9 + 24*x + 2*x^2)*exp(x). - _G. C. Greubel_, May 30 2024
%t A154600 LinearRecurrence[{3, -3, 1}, {33, 61, 93}, 50] (* _Vincenzo Librandi_, Feb 26 2012 *)
%t A154600 4*Binomial[Range[50]+6,2] - 51 (* _G. C. Greubel_, May 30 2024 *)
%o A154600 (PARI) a(n)=2*n*(n+22)+9 \\ _Charles R Greathouse IV_, Jan 11 2012
%o A154600 (Magma) I:=[33, 61, 93]; [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 26 2012
%o A154600 (SageMath) [2*n^2+22*n+9 for n in range(1,51)] # _G. C. Greubel_, May 30 2024
%Y A154600 Cf. A144562.
%K A154600 nonn,easy
%O A154600 1,1
%A A154600 _Vincenzo Librandi_, Jan 12 2009