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Search: id:A120892
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| A120892 |
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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. |
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+0
4
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| 1, 0, 3, 8, 33, 120, 451, 1680, 6273, 23408, 87363, 326040, 1216801, 4541160, 16947843, 63250208, 236052993, 880961760, 3287794051, 12270214440, 45793063713, 170902040408, 637815097923, 2380358351280, 8883618307201
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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.
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LINKS
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J. P. Chabert, Right Triangle Applet (Hypotenuse & angles computation, given legs<350)
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FORMULA
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Union of A045899 and A011922.
O.g.f.: -(-1+3*x)/((x+1)*(x^2-4*x+1)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
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CROSSREFS
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Sequence in context: A091831 A148916 A148917 this_sequence A109655 A001120 A117722
Adjacent sequences: A120889 A120890 A120891 this_sequence A120893 A120894 A120895
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 13 2006
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EXTENSIONS
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Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
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