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 A140413 #31 Jun 03 2024 18:25:17
%S A140413 1,1,9,33,145,609,2585,10945,46369,196417,832041,3524577,14930353,
%T A140413 63245985,267914297,1134903169,4807526977,20365011073,86267571273,
%U A140413 365435296161,1548008755921,6557470319841,27777890035289,117669030460993,498454011879265,2111485077978049
%N A140413 a(2n) = A000045(6n) + 1, a(2n+1) = A000045(6n+3) - 1.
%H A140413 Colin Barker, <a href="/A140413/b140413.txt">Table of n, a(n) for n = 0..1000</a>
%H A140413 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,5,1).
%F A140413 a(n) = A141325(3*n) = (-1)^n + A014445(n).
%F A140413 a(n) = +3*a(n-1) +5*a(n-2) +a(n-3). - _R. J. Mathar_, Dec 17 2010
%F A140413 G.f.: (1-x)^2 / ( (1+x)*(1-4*x-x^2) ). - _R. J. Mathar_, Dec 17 2010
%F A140413 a(n) = ((-1)^n + (-(2-sqrt(5))^n + (2+sqrt(5))^n) / sqrt(5)). - _Colin Barker_, Jun 06 2017
%F A140413 a(n) = -A033887(n) + 2*Sum_{k=0..n} A033887(k)*(-1)^(n-k). - Yomna Bakr and _Greg Dresden_, Jun 03 2024
%t A140413 LinearRecurrence[{3,5,1},{1,1,9},30] (* or *) CoefficientList[Series[ (1-x)^2/((1+x)(1-4*x-x^2)),{x,0,30}],x] (* _Harvey P. Dale_, Jun 20 2011 *)
%o A140413 (PARI) Vec((1-x)^2/((1+x)*(1-4*x-x^2)) + O(x^30)) \\ _Colin Barker_, Jun 06 2017
%o A140413 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-x)^2/((1+x)*(1-4*x-x^2)) )); // _G. C. Greubel_, Jun 08 2019
%o A140413 (Sage) ((1-x)^2/((1+x)*(1-4*x-x^2))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 08 2019
%o A140413 (GAP) a:=[1,1,9];; for n in [4..30] do a[n]:=3*a[n-1]+5*a[n-2]+a[n-3]; od; a; # _G. C. Greubel_, Jun 08 2019
%Y A140413 Cf. A000045, A014445, A141325.
%K A140413 nonn,easy
%O A140413 0,3
%A A140413 _Paul Curtz_, Jun 17 2008