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 A169592 #14 Oct 23 2024 14:39:12
%S A169592 1,2,2,2,7,4,7,16,12,12,47,20,33,114,54,54,331,88,143,872,232,232,
%T A169592 2563,376,609,7170,986,986,21279,1596,2583,61632,4180,4180,183911,
%U A169592 6764,10945,542386,17710,17710,1622979,28656,46367,4829336,75024,75024,14470299,121392
%N A169592 Expansion of 1/((1-x)*(1-x^2-x^4)) + x/(1-3*x^3).
%H A169592 G. C. Greubel, <a href="/A169592/b169592.txt">Table of n, a(n) for n = 0..1000</a>
%H A169592 Philippe Flajolet and Robert Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html">Analytic Combinatorics</a>, Cambridge Univ. Press, 2009, page 303.
%H A169592 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,2,-2,-4,3,-3,3).
%F A169592 G.f.: (1+x+x^4-x^5+x^6-x^2-4*x^3)/((1-x)*(1-3*x^3)*(1-x^2-x^4)).
%F A169592 a(n) = +a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) +3*a(n-6) -3*a(n-7) 3*a(n-8).
%F A169592 a(n) = A103609(n+6) - 1 + 3^((n-1)/3) if n == 1 mod 3.
%F A169592 a(n) = A103609(n+6) - 1 if n == 0 or 2 mod 3.
%t A169592 p[t_]= 1/((1-t)*(1-t^2-t^4)) + t/(1-3*t^3);
%t A169592 CoefficientList[ Series[p[t], {t, 0, 60}], t]
%o A169592 (Magma)
%o A169592 R<x>:=PowerSeriesRing(Integers(), 60);
%o A169592 Coefficients(R!( 1/((1-x)*(1-x^2-x^4)) +x/(1-3*x^3) )); // _G. C. Greubel_, Oct 23 2024
%o A169592 (SageMath)
%o A169592 def A169592_list(prec):
%o A169592 P.<x> = PowerSeriesRing(ZZ, prec)
%o A169592 return P( 1/((1-x)*(1-x^2-x^4)) +x/(1-3*x^3) ).list()
%o A169592 A169592_list(60) # _G. C. Greubel_, Oct 23 2024
%Y A169592 Cf. A103609.
%K A169592 nonn,easy
%O A169592 0,2
%A A169592 _Roger L. Bagula_, Dec 02 2009
%E A169592 Notation adapted to OEIS standards, sequence extended, formulas added by the Assoc. Editors of the OEIS [Dec 05 2009]