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%I #29 Sep 08 2022 08:45:34
%S 1,0,0,1,1,1,1,4,4,1,13,13,1,40,40,1,121,121,1,364,364,1,1093,1093,1,
%T 3280,3280,1,9841,9841,1,29524,29524,1,88573,88573,1,265720,265720,1,
%U 797161,797161,1,2391484,2391484,1,7174453,7174453,1,21523360,21523360,1,64570081
%N First differences of A140298.
%H Andrew Howroyd, <a href="/A140313/b140313.txt">Table of n, a(n) for n = 0..1000</a>
%F Mix 1, A003462(n), A003462(n).
%F G.f.: (x - 1)*(x^3 + 3*x^2 + 2*x + 1)/((3*x^3 - 1)*(x^2 + x + 1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009
%t CoefficientList[Series[(x - 1) (x^3 + 3 x^2 + 2 x + 1)/((3 x^3 - 1) (x^2 + x + 1)), {x, 0, 52}], x] (* _Michael De Vlieger_, Nov 05 2018 *)
%o (PARI) Vec((1 - x)*(1 + 2*x + 3*x^2 + x^3)/((1 - 3*x^3)*(1 + x + x^2)) + O(x^40)) \\ _Andrew Howroyd_, Nov 03 2018
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (x-1)*(x^3+3*x^2+2*x+1)/((3*x^3-1)*(x^2+x+1)) )); // _G. C. Greubel_, Nov 21 2018
%o (Sage) s=((x-1)*(x^3+3*x^2+2*x+1)/((3*x^3-1)*(x^2+x+1))).series(x,50);
%o s.coefficients(x, sparse=False) # _G. C. Greubel_, Nov 21 2018
%Y Cf. A140298
%K nonn
%O 0,8
%A _Paul Curtz_, May 25 2008
%E Terms a(33) and beyond from _Andrew Howroyd_, Nov 03 2018
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