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A077244
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Bisection (odd part) of Chebyshev sequence with Diophantine property.
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4
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3, 22, 173, 1362, 10723, 84422, 664653, 5232802, 41197763, 324349302, 2553596653, 20104423922, 158281794723, 1246149933862, 9810917676173, 77241191475522, 608118614128003, 4787707721548502, 37693543158260013
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OFFSET
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0,1
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COMMENTS
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3*a(n)^2 - 5*b(n)^2 = 7, with the companion sequence b(n)= A077243(n).
The even part is A077246(n) with Diophantine companion A077245(n).
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LINKS
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Table of n, a(n) for n=0..18.
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n)= (2*T(n+1, 4)+T(n, 4))/3, with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 4)= A001091(n).
G.f.: (3-2*x)/(1-8*x+x^2).
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EXAMPLE
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22 = a(1) = sqrt((5*A077243(1)^2 + 7)/3) = sqrt((5*17^2 + 7)/3) = sqrt(484) = 22.
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CROSSREFS
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Sequence in context: A192365 A074578 A074576 * A138899 A132595 A065204
Adjacent sequences: A077241 A077242 A077243 * A077245 A077246 A077247
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Nov 08 2002
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STATUS
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approved
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