%I #9 Jun 17 2023 07:50:34
%S 4,2,-2,12,12,10,54,68,108,282,422,772,1604,2674,5006,9580,16884,
%T 31506,58606,105948,196508,362298,662022,1222772,2249116,4127210,
%U 7605718,13984148,25701652,47311458,86994846,159975004,294336612,541281698,995529822,1831291692,3367998380,6194717674
%N Sum of generalized tribonacci numbers A001644 and inverted tribonacci numbers A075298.
%C It seems that aside from a(2) the sequence is nonnegative.
%H G. C. Greubel, <a href="/A075418/b075418.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 4, 1, 0, -1).
%F a(n) = a(n-2) + 4*a(n-3) + a(n-4) - a(n-6), a(0)=4, a(1)=2, a(2)=-2, a(3)=12, a(4)=12, a(5)=10.
%F O.g.f.: (4 + 2*x - 6*x^2 - 6*x^3 + 2*x^4 + 4*x^5)/(1 - x^2 - 4*x^3 - x^4 + x^6).
%t CoefficientList[Series[(4+2x-6x^2-6x^3+2x^4+4x^5)/(1-x^2-4x^3-x^4+x^6), {x, 0, 40}], x]
%o (PARI) my(x='x+O('x^40)); Vec((4+2*x-6*x^2-6*x^3+2*x^4+4*x^5)/(1-x^2 -4*x^3-x^4+x^6)) \\ _G. C. Greubel_, Apr 21 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (4+2*x-6*x^2-6*x^3+2*x^4+4*x^5)/(1-x^2-4*x^3-x^4+x^6) )); // _G. C. Greubel_, Apr 21 2019
%o (Sage) ((4+2*x-6*x^2-6*x^3+2*x^4+4*x^5)/(1-x^2-4*x^3-x^4+x^6)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 21 2019
%Y Cf. A001644, A075298.
%K easy,sign
%O 0,1
%A Mario Catalani (mario.catalani(AT)unito.it), Sep 14 2002