Search: id:A120892
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%I A120892
%S A120892 1,0,3,8,33,120,451,1680,6273,23408,87363,326040,1216801,4541160,
%T A120892 16947843,63250208,236052993,880961760,3287794051,12270214440,
%U A120892 45793063713,170902040408,637815097923,2380358351280,8883618307201
%N A120892 a(n)=3*a(n-1)+3*a(n-2)-a(n-3);a(0)=1,a(1)=0,a(2)=3. a(n)=4*{a(n-1)+(-1)^n}-a(n-2);
               a(0)=1,a(1)=0.
%C A120892 For n>1, short leg of primitive Pythagorean triangles having an angle 
               nearing pi/3 with larger values of sides.[Complete triple (X,Y,Z),
               X<Y<Z is given by X=a(n),Y=A001353(n),Z=A120893(n), with recurrence 
               relations Y(i+1)=2*{Y(i)-(-1)^i} + 3*a(i) ; Z(i+1)=2*{2*Z(i)-a(i-1)} 
               - 3*(-1)^i] A120893(n)=2*a(n)-(-1)^n.
%H A120892 J. P. Chabert, <a href="http://jpm-chabert.club.fr/maths/Triangle_rect.htm">
               Right Triangle Applet (Hypotenuse & angles computation, given legs<350)</
               a>
%F A120892 Union of A045899 and A011922.
%F A120892 O.g.f.: -(-1+3*x)/((x+1)*(x^2-4*x+1)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 23 2007
%Y A120892 Sequence in context: A091831 A148916 A148917 this_sequence A109655 A001120 
               A117722
%Y A120892 Adjacent sequences: A120889 A120890 A120891 this_sequence A120893 A120894 
               A120895
%K A120892 nonn
%O A120892 0,3
%A A120892 Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 13 2006
%E A120892 Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006

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