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Search: id:A097776
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| A097776 |
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Pell equation solutions (14*b(n))^2 - 197*a(n)^2 = -1 with b(n):=A097775(n), n>=0. |
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+0
4
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| 1, 785, 617009, 484968289, 381184458145, 299610499133681, 235493471134615121, 185097568701308351425, 145486453505757229604929, 114352167357956481161122769, 89880658056900288435412891505
(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*393) - S(n-1, 2*393) = T(2*n+1, sqrt(197))/sqrt(197), with Chebyshev polynomials of the 2nd and first kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x); and A053120 for the T-triangle.
a(n)= ((-1)^n)*S(2*n, 28*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.
G.f.: (1-x)/(1-786*x+x^2).
a(n)=786*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=785 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
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(x,y) = (14*1=14;1), (11018=14*787;785), (8660134=14*618581;617009), ... give the positive integer solutions to x^2 - 197*y^2 =-1.
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CROSSREFS
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Cf. A097774 for S(n, 786).
Sequence in context: A159896 A031734 A031616 this_sequence A031526 A108795 A097774
Adjacent sequences: A097773 A097774 A097775 this_sequence A097777 A097778 A097779
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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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