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 A154599 #29 May 30 2024 06:57:05
%S A154599 30,56,86,120,158,200,246,296,350,408,470,536,606,680,758,840,926,
%T A154599 1016,1110,1208,1310,1416,1526,1640,1758,1880,2006,2136,2270,2408,
%U A154599 2550,2696,2846,3000,3158,3320,3486,3656,3830,4008,4190,4376,4566,4760,4958,5160
%N A154599 a(n) = 2*n^2 + 20*n + 8.
%C A154599 Tenth diagonal of A144562.
%C A154599 2*a(n) + 84 is a square.
%H A154599 Vincenzo Librandi, <a href="/A154599/b154599.txt">Table of n, a(n) for n = 1..1000</a>
%H A154599 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A154599 From _R. J. Mathar_, Jan 05 2011: (Start)
%F A154599 a(n) = 2*A127147(n+13).
%F A154599 G.f.: 2*x*(5-4*x)*(3-x)/(1-x)^3. (End)
%F A154599 From _Amiram Eldar_, Feb 25 2023: (Start)
%F A154599 Sum_{n>=1} 1/a(n) = 79/952 - cot(sqrt(21)*Pi)*Pi/(4*sqrt(21)).
%F A154599 Sum_{n>=1} (-1)^(n+1)/a(n) = 2851/14280 - cosec(sqrt(21)*Pi)*Pi/(4*sqrt(21)). (End)
%F A154599 E.g.f.: 2*(-4 + (4 + 11*x + x^2)*exp(x)). - _G. C. Greubel_, May 30 2024
%t A154599 LinearRecurrence[{3, -3, 1}, {30, 56, 86}, 50] (* _Vincenzo Librandi_, Feb 26 2012 *)
%t A154599 Table[2n^2+20n+8,{n,50}] (* _Harvey P. Dale_, Jun 15 2019 *)
%o A154599 (Magma) I:=[30, 56, 86]; [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 A154599 (PARI) for(n=1, 40, print1(2*n^2+20*n+8", ")); \\ _Vincenzo Librandi_, Feb 26 2012
%o A154599 (SageMath) [2*n^2+20*n+8 for n in range(1,41)] # _G. C. Greubel_, May 30 2024
%Y A154599 Cf. A067076, A127147, A144562, A153238.
%K A154599 nonn,easy
%O A154599 1,1
%A A154599 _Vincenzo Librandi_, Jan 12 2009