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 A166753 #19 Aug 12 2024 18:44:46
%S A166753 1,2,5,6,17,18,61,62,233,234,917,918,3649,3650,14573,14574,58265,
%T A166753 58266,233029,233030,932081,932082,3728285,3728286,14913097,14913098,
%U A166753 59652341,59652342,238609313,238609314,954437197,954437198,3817748729,3817748730
%N A166753 Partial sums of A166752.
%H A166753 G. C. Greubel, <a href="/A166753/b166753.txt">Table of n, a(n) for n = 0..1000</a>
%H A166753 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,-5,-4,4).
%F A166753 G.f.: (1+x-2*x^2-4*x^3)/((1-x)*(1-5*x^2+4*x^4)).
%F A166753 a(n) = a(n+1) + 5*a(n+2) - 5*a(n-3) - 4*a(n-4) + 4*a(n-5).
%F A166753 a(n) = (4/3)*A061547(n+1) - (1/3)*A166754(n).
%F A166753 a(n) = (4/3)*A061547(n+1) - (1/3)*A000975(n) + (4/3)*A011377(n-2).
%t A166753 LinearRecurrence[{1,5,-5,-4,4}, {1,2,5,6,17}, 40] (* _G. C. Greubel_, May 24 2016 *)
%t A166753 Accumulate[LinearRecurrence[{0,5,0,-4},{1,1,3,1},40]] (* _Harvey P. Dale_, Aug 12 2024 *)
%o A166753 (PARI) my(x='x+O('x^40)); Vec((1+x-2*x^2-4*x^3)/((1-x)*(1-5*x^2+4*x^4))) \\ _G. C. Greubel_, Sep 30 2017
%o A166753 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x-2*x^2-4*x^3)/((1-x)*(1-5*x^2+4*x^4)) )); // _G. C. Greubel_, Jun 06 2019
%o A166753 (Sage) ((1+x-2*x^2-4*x^3)/((1-x)*(1-5*x^2+4*x^4))).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 06 2019
%K A166753 easy,nonn
%O A166753 0,2
%A A166753 _Paul Barry_, Oct 21 2009