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G.f.: ((1-q)^2+(1+q)*sqrt(1-6*q+q^2))/2.
4

%I #18 Jan 05 2025 19:51:39

%S 1,-2,-3,-8,-28,-112,-484,-2200,-10364,-50144,-247684,-1243816,

%T -6331164,-32591184,-169376484,-887465784,-4682990076,-24864759744,

%U -132745182724,-712136879944,-3837043171100,-20755343638064,-112668274522852,-613581530620888,-3351355226348668,-18354390999804832,-100771410237846404,-554536090460808680

%N G.f.: ((1-q)^2+(1+q)*sqrt(1-6*q+q^2))/2.

%H Harris Kwong, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/48-4/Kwong.pdf">On recurrences of Fahr and Ringel: an alternate approach</a>, Fibonacci Quart. 48 (2010), no. 4, 363-365; see p. 364.

%t CoefficientList[Series[((1 - x)^2 + (1 + x) Sqrt[1 - 6 x + x^2])/2, {x, 0, 27}], x] (* _Michael De Vlieger_, Oct 12 2016 *)

%Y Cf. A010683 (a closely-related g.f.)

%K sign

%O 0,2

%A _N. J. A. Sloane_, Dec 08 2010