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 A084156 #21 Oct 10 2022 15:28:19
%S A084156 0,1,2,13,44,181,662,2521,9368,35113,130922,489061,1824836,6811741,
%T A084156 25420670,94875313,354076208,1321442641,4931681234,18405321661,
%U A084156 68689566044,256353060613,956722558310,3570537526921,13325427195080,49731172316281,185599261007162
%N A084156 Binomial transform of sinh(x)*cosh(sqrt(3)*x).
%H A084156 Vincenzo Librandi, <a href="/A084156/b084156.txt">Table of n, a(n) for n = 0..200</a>
%H A084156 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,2,-12,3).
%F A084156 a(n) = 4*a(n-1) + 2*a(n-2) - 12*a(n-3) + 3*a(n-4).
%F A084156 a(n) = ((2+sqrt(3))^n + (2-sqrt(3))^n - (sqrt(3))^n - (-sqrt(3))^n)/4.
%F A084156 G.f.: x*(1-2*x+3*x^2)/((1-3*x^2)(1-4*x+x^2)).
%F A084156 E.g.f. : exp(x)*sinh(x)*cosh(sqrt(3)*x).
%F A084156 a(n) = (2*ChebyshevT(n, 2) - (1+(-1)^n)*3^(n/2))/4 = (A001075(n) - A254006(n))/2. - _G. C. Greubel_, Oct 10 2022
%p A084156 seq((2*simplify(ChebyshevT(n,2)) - (1+(-1)^n)*3^(n/2))/4, n = 0..30); # _G. C. Greubel_, Oct 10 2022
%t A084156 LinearRecurrence[{4,2,-12,3},{0,1,2,13},30] (* _Harvey P. Dale_, Feb 01 2014 *)
%o A084156 (Magma) I:=[0,1,2,13]; [n le 4 select I[n] else 4*Self(n-1)+2*Self(n-2)-12*Self(n-3)+3*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Feb 13 2014
%o A084156 (SageMath)
%o A084156 def A084156(n): return (chebyshev_T(n, 2) - ((n+1)%2)*3^(n/2))/2
%o A084156 [A084156(n) for n in range(31)] # _G. C. Greubel_, Oct 10 2022
%Y A084156 Cf. A001075, A084154, A084157, A254006.
%K A084156 nonn,easy
%O A084156 0,3
%A A084156 _Paul Barry_, May 16 2003