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 A027000 #33 Jul 25 2025 08:18:02
%S A027000 1,13,54,171,487,1324,3525,9297,24418,64015,167691,439128,1149769,
%T A027000 3010261,7881102,20633139,54018415,141422212,370248333,969322905,
%U A027000 2537720506,6643838743,17393795859,45537548976,119218851217,312119004829
%N A027000 a(n) = Lucas(2*n+3) - (6*n+4).
%H A027000 Nathaniel Johnston, <a href="/A027000/b027000.txt">Table of n, a(n) for n = 1..600</a>
%H A027000 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,5,-1).
%F A027000 a(n) = A026998(2*n, n+1).
%F A027000 a(n) = 4*F(2*n-1) + 7*F(2*n) - 6*n - 4, with F(n) = A000045(n) (Fibonacci). - _Ralf Stephan_, Feb 07 2004
%F A027000 G.f.: x*(1+8*x-3*x^2) / ((1-x)^2*(1-3*x+x^2)). - _Franklin T. Adams-Watters_ and _D. S. McNeil_, Dec 16 2011
%F A027000 E.g.f.: 2*exp(3*x/2)*( 2*cosh(p*x) + 2*p*sinh(p*x) - (3*x+2)*exp(-x/2) ), where 2*p = sqrt(5). - _G. C. Greubel_, Jul 20 2025
%t A027000 Table[LucasL[2n + 3] - (6n + 4), {n, 30}] (* _Alonso del Arte_, Dec 16 2011 *)
%o A027000 (Magma) [ Lucas(2*n+3) - (6*n+4): n in [1..100]]; // _Vincenzo Librandi_, Apr 15 2011
%o A027000 (SageMath)
%o A027000 def A027000(n): return lucas_number2(2*n+3,1,-1) -2*(3*n+2) # _G. C. Greubel_, Jul 20 2025
%Y A027000 Cf. A000032, A000045, A026998.
%K A027000 nonn
%O A027000 1,2
%A A027000 _Clark Kimberling_
%E A027000 a(23) - a(26) from _Vincenzo Librandi_, Apr 15 2011