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Search: id:A097772
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| A097772 |
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Pell equation solutions (13*a(n))^2 - 170*b(n)^2 = -1 with b(n):=A097771(n), n>=0. |
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3
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| 1, 679, 460361, 312124079, 211619665201, 143477820882199, 97277750938465721, 65954171658458876639, 44716831106684179895521, 30317945536160215510286599, 20555522356685519431794418601
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n)= S(n, 2*339) + S(n-1, 2*339) = S(2*n, 2*sqrt(170)), with Chebyshev polynomials of the 2nd kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x).
a(n)= ((-1)^n)*T(2*n+1, 13*I)/(13*I) with the imaginary unit I and Chebyshev polynomials of the first kind. See the T-triangle A053120.
G.f.: (1+x)/(1-2*339*x+x^2).
a(n)=678*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=679 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
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(x,y) = (13*1=13;1), (8827=13*679;677), (5984693=13*460361;459005), ... give the positive integer solutions to x^2 - 170*y^2 =-1.
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CROSSREFS
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Cf. A097771 for S(n, 2*339).
Sequence in context: A121105 A046514 A164650 this_sequence A154036 A118509 A043691
Adjacent sequences: A097769 A097770 A097771 this_sequence A097773 A097774 A097775
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004
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