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%I #17 Sep 08 2022 08:45:48
%S 1,2,5,6,17,18,61,62,233,234,917,918,3649,3650,14573,14574,58265,
%T 58266,233029,233030,932081,932082,3728285,3728286,14913097,14913098,
%U 59652341,59652342,238609313,238609314,954437197,954437198,3817748729,3817748730
%N Partial sums of A166752.
%H G. C. Greubel, <a href="/A166753/b166753.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,-5,-4,4).
%F G.f.: (1+x-2*x^2-4*x^3)/((1-x)*(1-5*x^2+4*x^4)).
%F a(n) = a(n+1) + 5*a(n+2) - 5*a(n-3) - 4*a(n-4) + 4*a(n-5).
%F a(n) = (4/3)*A061547(n+1) - (1/3)*A166754(n).
%F a(n) = (4/3)*A061547(n+1) - (1/3)*A000975(n) + (4/3)*A011377(n-2).
%t LinearRecurrence[{1,5,-5,-4,4}, {1,2,5,6,17}, 40] (* _G. C. Greubel_, May 24 2016 *)
%o (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 (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 (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 easy,nonn
%O 0,2
%A _Paul Barry_, Oct 21 2009
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