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Search: id:A077413
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| A077413 |
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Bisection (odd part) of Chebyshev sequence with Diophantine property. |
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+0
5
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| 2, 13, 76, 443, 2582, 15049, 87712, 511223, 2979626, 17366533, 101219572, 589950899, 3438485822, 20040964033, 116807298376, 680802826223, 3968009658962, 23127255127549, 134795521106332, 785645871510443
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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-8*a(n)^2 + b(n)^2 = 17, with the companion sequence b(n)= A077239(n).
The even part is A054488(n) with Diophantine companion A077240(n).
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LINKS
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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) := -1, a(0)=2.
a(n)= 2*S(n, 6)+S(n-1, 6), with S(n, x) := U(n, x/2), Chebyshev polynomials of 2nd kind, A049310. S(n, 6)= A001109(n+1).
G.f.: (2+x)/(1-6*x+x^2).
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EXAMPLE
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8*a(1)^2 + 17 = 8*13^2+17 = 1369 = 37^2 = A077239(1)^2.
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CROSSREFS
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Cf. A077241 (even and odd parts).
Adjacent sequences: A077410 A077411 A077412 this_sequence A077414 A077415 A077416
Sequence in context: A154357 A161130 A007509 this_sequence A024199 A037523 A037732
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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.uni-karlsruhe.de), Nov 08 2002
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