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A098258
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Chebyshev polynomials S(n,531) + S(n-1,531) with Diophantine property.
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2
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1, 532, 282491, 150002189, 79650879868, 42294467207719, 22458282436418921, 11925305679271239332, 6332314857410591666371, 3362447263979344903603669, 1785453164858174733221881868, 948072268092426803995915668239
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OFFSET
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0,2
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COMMENTS
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(23*a(n))^2 - 533*b(n)^2 = -4 with b(n)=A098259(n) give all positive solutions of this Pell equation.
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LINKS
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Table of n, a(n) for n=0..11.
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, 531) + S(n-1, 531) = S(2*n, sqrt(533)), with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x). S(n, 531)=A098257(n).
a(n)= (-2/23)*I*((-1)^n)*T(2*n+1, 23*I/2) with the imaginary unit I and Chebyshev's polynomials of the first kind. See the T-triangle A053120.
G.f.: (1+x)/(1-531*x+x^2).
a(n)=531*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=532 . [From Philippe DELEHAM, Nov 18 2008]
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EXAMPLE
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All positive solutions of Pell equation x^2 - 533*y^2 = -4 are
(23=23*1,1), (12236=23*532,530), (6497293=23*282491,281429),
(3450050347=23*150002189,149438269), ...
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CROSSREFS
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Sequence in context: A191950 A048055 A067803 * A160176 A077085 A165989
Adjacent sequences: A098255 A098256 A098257 * A098259 A098260 A098261
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Sep 10 2004
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STATUS
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approved
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