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A077240
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Bisection (even part) of Chebyshev sequence with Diophantine property.
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4
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5, 23, 133, 775, 4517, 26327, 153445, 894343, 5212613, 30381335, 177075397, 1032071047, 6015350885, 35060034263, 204344854693, 1191009093895, 6941709708677, 40459249158167, 235813785240325, 1374423462283783
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OFFSET
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0,1
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COMMENTS
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a(n)^2 - 8*b(n)^2 = 17, with the companion sequence b(n)= A054488(n).
The odd part is A077239(n) with Diophantine companion A077413(n).
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LINKS
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Table of n, a(n) for n=0..19.
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)= 6*a(n-1) - a(n-2), a(-1) := 7, a(0)=5.
a(n)= T(n+1, 3)+2*T(n, 3), with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 3)= A001541(n).
G.f.: (5-7*x)/(1-6*x+x^2).
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EXAMPLE
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23 = a(1) = sqrt(8*A054488(1)^2 + 17) = sqrt(8*8^2 + 17)= sqrt(529) = 23.
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CROSSREFS
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Cf. A077242 (even and odd parts).
Sequence in context: A186755 A009321 A078509 * A129098 A047049 A020034
Adjacent sequences: A077237 A077238 A077239 * A077241 A077242 A077243
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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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