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 A027286 #23 Apr 21 2023 03:23:25
%S A027286 1,4,18,56,190,564,1722,4976,14454,40940,115698,322728,896558,2471588,
%T A027286 6786090,18537184,50459366,136844892,370030434,997705240,2683514526,
%U A027286 7201203988,19284880794,51546789456,137541880150,366412976332
%N A027286 a(n) = Sum_{k=0..2n} (k+1) * A026584(n, k).
%H A027286 G. C. Greubel, <a href="/A027286/b027286.txt">Table of n, a(n) for n = 0..1000</a>
%H A027286 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,7,-8,-16).
%F A027286 G.f.: (1+2*x+3*x^2)/(1-x-4*x^2)^2.
%F A027286 From _G. C. Greubel_, Dec 12 2021: (Start)
%F A027286 a(n) = 2^(n-3)*( -6*F(n+1, 1/2) + Sum_{j=0..n} F(n-j+1, 1/2)*( 14*F(j+1, 1/2) + 5*F(j, 1/2) ), where F(n, x) are the Fibonacci polynomials.
%F A027286 a(n) = (2^(n-1)/17)*(n+1)*( 14*L(n+2, 1/2) + 5*L(n+1, 1/2) ), where L(n, x) are the Lucas polynomials.
%F A027286 a(n) = 2*a(n-1) + 7*a(n-2) - 8*a(n-3) - 16*a(n-4). (End)
%t A027286 LinearRecurrence[{2,7,-8,-16},{1,4,18,56}, 30] (* _G. C. Greubel_, Dec 12 2021 *)
%o A027286 (Magma) I:=[1,4,18,56]; [n le 4 select I[n] else 2*Self(n-1) +7*Self(n-2) -8*Self(n-3) -16*Self(n-4): n in [1..31]]; // _G. C. Greubel_, Dec 12 2021
%o A027286 (Sage) [2^(n-1)*(n+1)*(14*lucas_number2(n+2, 1/2, -1) + 5*lucas_number2(n+1, 1/2, -1))/17 for n in (0..30)] # _G. C. Greubel_, Dec 12 2021
%o A027286 (PARI) a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; -16,-8,7,2]^n*[1;4;18;56])[1,1] \\ _Charles R Greathouse IV_, Oct 21 2022
%Y A027286 Cf. A000032, A000045, A006131, A026584, A072265.
%K A027286 nonn,easy
%O A027286 0,2
%A A027286 _Clark Kimberling_