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%I #13 Sep 08 2022 08:45:49
%S 0,1,1,9,19,100,279,1189,3781,14661,49600,184141,641421,2333629,
%T 8240959,29700900,105561739,378777169,1350292761,4835148121,
%U 17260998400,61748847081,220582688041,788748162049,2818480203099,10076047502500
%N G.f. -x*(x-1)*(1+x)/(1-x-9*x^2-x^3+x^4).
%C The member k=9 of a family of sequences starting 0,1,1,k with recurrence a(n) = a(n-1)+k*a(n-2)+a(n-3)-a(n-4).
%H Vincenzo Librandi, <a href="/A171066/b171066.txt">Table of n, a(n) for n = 0..1000</a>
%H Hugh Williams, R. K. Guy, <a href="http://dx.doi.org/10.1142/S1793042111004587">Some fourth-order linear divisibility sequences</a>, Intl. J. Number Theory vol. 7 (5) (2011) 1255-1277
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,9,1,-1).
%F a(n)= +a(n-1) +9*a(n-2) +a(n-3) -a(n-4)
%t CoefficientList[Series[-x*(x - 1)*(1 + x)/(1 - x - 9*x^2 - x^3 + x^4), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 19 2012 *)
%o (Magma) I:=[0, 1, 1, 9]; [n le 4 select I[n] else Self(n-1) + 9*Self(n-2) + Self(n-3) - Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 19 2012
%Y Cf. A116201 (k=1), A105309 (k=2), A152090 (k=3), A007598 (k=4), A005178 (k=5), A003757 (k=6).
%K nonn,easy
%O 0,4
%A R. J. Mathar, at the request of _R. K. Guy_, Sep 03 2010
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