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 A358027 #33 Mar 24 2025 04:11:35
%S A358027 1,2,3,6,11,20,35,62,107,188,323,566,971,1700,2915,5102,8747,15308,
%T A358027 26243,45926,78731,137780,236195,413342,708587,1240028,2125763,
%U A358027 3720086,6377291,11160260,19131875,33480782,57395627
%N A358027 Expansion of g.f.: (1 + x - 2*x^2 + 2*x^4)/((1-x)*(1-3*x^2)).
%H A358027 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3).
%F A358027 a(n) = (1/3)*(2*[n=0] + 2*[n=1] - 3 + 4*A254006(n) + 7*A254006(n-1)).
%F A358027 a(n) = a(n-1) - 3*a(n-2) + 3*a(n-3), for n >= 5.
%F A358027 E.g.f.: (1/3)*( 2 + 2*x - 3*exp(x) + 4*cosh(sqrt(3)*x) + (7/sqrt(3))*sinh(sqrt(3)*x) ).
%F A358027 G.f.: (1 +x -2*x^2 +2*x^4)/((1-x)*(1-3*x^2)). - _Clark Kimberling_, Oct 31 2022
%t A358027 LinearRecurrence[{1,3,-3}, {1,2,3,6,11}, 61]
%o A358027 (Magma) I:=[3,6,11]; [1,2] cat [n le 3 select I[n] else Self(n-1) +3*Self(n-2) -3*Self(n-3): n in [1..60]];
%o A358027 (SageMath)
%o A358027 def A254006(n): return 3^(n/2)*(1 + (-1)^n)/2
%o A358027 def A358027(n): return (1/3)*( 4*A254006(n) + 7*A254006(n-1) +2*int(n==0) + 2*int(n==1) - 3 )
%o A358027 [A358027(n) for n in (0..60)]
%Y A358027 Cf. A052993, A062318, A164123, A254006.
%K A358027 easy,nonn
%O A358027 0,2
%A A358027 _G. C. Greubel_, Oct 31 2022