%I A120893
%S A120893 1,1,5,17,65,241,901,3361,12545,46817,174725,652081,2433601,9082321,
%T A120893 33895685,126500417,472105985,1761923521,6575588101,24540428881,
%U A120893 91586127425,341804080817,1275630195845,4760716702561,17767236614401
%N A120893 a(n)=3*a(n-1) + 3*a(n-2) - a(n-3) ; a(0)=1,a(1)=1,a(2)=5.
%C A120893 For n>1,hypotenuse of primitive Pythagorean triangles having an angle 
               nearing pi/3 for larger values of sides.[Complete triple (X,Y,Z),
               X<Y<Z is given by X=A120892(n),Y=A001353(n),Z=a(n) with recurrence 
               relations X(i+1)=2*{a(i)-(-1)^i}-X(i-1) ; Y(i+1)=2*T(i)-T(i-1)-(-1)^i, 
               where T(i)=Y(i)+a(i)] a(n)=2*A120892(n)-(-1)^n.
%F A120893 Union of A103772 and A103974. a(n)=2*{2*a(n-1) + (-1)^n} - a(n-2) ; a(0)=1,
               a(1)=1.
%F A120893 a(n)=[(-1)^n+(2-sqrt(3))^n+(2+sqrt(3))^n]/3. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Jul 24 2006
%F A120893 O.g.f: -(-1+2*x+x^2)/((1+x)*(x^2-4*x+1)) = (1/3)/(1+x)+(1/3)*(-4*x+2)/
               (x^2-4*x+1) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 
               02 2007
%p A120893 a[0]:=1: a[1]:=1: a[2]:=5: for n from 3 to 40 do a[n]:=3*a[n-1]+3*a[n-2]-a[n-3] 
               od: seq(a[n],n=0..30); - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Jul 24 2006
%Y A120893 Sequence in context: A149670 A149671 A062229 this_sequence A149672 A149673 
               A046231
%Y A120893 Adjacent sequences: A120890 A120891 A120892 this_sequence A120894 A120895 
               A120896
%K A120893 nonn
%O A120893 0,3
%A A120893 Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 14 2006
%E A120893 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 24 2006