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%I A144044 #6 Feb 04 2021 09:37:44
%S A144044 1,4,196,2304,55696,906304,18181696,325730304,6199357696,114211554304,
%T A144044 2141141533696,39766241378304,742275639709696,13817991215202304,
%U A144044 257604225193885696,4798702283133026304,89428432275804061696
%N A144044 a(n) = ((1+sqrt(11))^n-(1-sqrt(11))^n)^2/44.
%C A144044 Sequences of the form a(n) = ((A+sqrt B)^n-(A-sqrt B)^n)^2/(4B) have recurrences a(n) = (3A^2+B) *a(n-1) +(B+3A^2)*(B-A^2) *a(n-2) -(B-A^2)^3*a(n-3) and generating functions x(1+(A^2-B)x) / ((1 -(A^2-B)x)(1-2(A^2+B)x +(A^4-2A^2B+B^2)x^2)). - _R. J. Mathar_, Nov 01 2008
%H A144044 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,140,-1000).
%F A144044 From _R. J. Mathar_, Nov 01 2008: (Start)
%F A144044 a(n) = 14*a(n-1)+140*a(n-2)-1000*a(n-3).
%F A144044 G.f. x(1-10x)/((10x+1)(1-24x+100x^2)). (End)
%K A144044 nonn,easy
%O A144044 1,2
%A A144044 Al Hakanson (hawkuu(AT)gmail.com), Sep 08 2008
%E A144044 More terms from _R. J. Mathar_, Nov 01 2008

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