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%I #13 Sep 08 2022 08:45:49
%S 0,1,1,11,23,144,407,2003,6601,28897,103104,425569,1582009,6337475,
%T 24062039,94930704,364368599,1426330907,5505254161,21464332033,
%U 83084090112,323270665729,1253154734833,4870751815931,18895640474711
%N G.f. -x*(x-1)*(1+x)/(1-x-11*x^2-x^3+x^4).
%C The member k=11 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="/A171068/b171068.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 (1,11,1,-1).
%F a(n)= +a(n-1) +11*a(n-2) +a(n-3) -a(n-4).
%t CoefficientList[Series[-x*(x - 1)*(1 + x)/(1 - x - 11*x^2 - x^3 + x^4), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 19 2012 *)
%o (Magma) I:=[0, 1, 1, 11]; [n le 4 select I[n] else Self(n-1) + 11*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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