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Search: id:A097735
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| A097735 |
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Pell equation solutions (8*a(n))^2 - 65*b(n)^2 = -1 with b(n):=A097736(n), n>=0. |
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3
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| 1, 259, 66821, 17239559, 4447739401, 1147499525899, 296050429942541, 76379863425649679, 19705708713387674641, 5083996468190594407699, 1311651383084459969511701, 338400972839322481539611159
(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*129) + S(n-1, 2*129) = S(2*n, 2*sqrt(65)), 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, 8*I)/(8*I) with the imaginary unit I and Chebyshev polynomials of the first kind. See the T-triangle A053120.
G.f.: (1+x)/(1-2*129*x+x^2).
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EXAMPLE
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(x,y) = (8,1), (2072,257), (534568,66305), ... give the positive integer solutions to x^2 - 65*y^2 =-1.
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CROSSREFS
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Cf. A097731 for S(n, 2*129).
Sequence in context: A038480 A022221 A121918 this_sequence A063485 A015929 A139408
Adjacent sequences: A097732 A097733 A097734 this_sequence A097736 A097737 A097738
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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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