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Search: id:A077236
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| A077236 |
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Bisection (even part) of Chebyshev sequence with diophantine property. |
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+0
5
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| 4, 11, 40, 149, 556, 2075, 7744, 28901, 107860, 402539, 1502296, 5606645, 20924284, 78090491, 291437680, 1087660229, 4059203236, 15149152715, 56537407624, 211000477781, 787464503500, 2938857536219, 10967965641376
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n)^2 - 3*b(n)^2 = 13, with the companion sequence b(n)= A054491(n).
The odd part is A077235(n) with diophantine companion A077234(n).
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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)= T(n+1, 2)+2*T(n, 2), with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 2)= A001075(n).
G.f.: (4-5*x)/(1-4*x+x^2).
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EXAMPLE
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11 = a(1) = sqrt(3*A054491(1)^2 + 13) = sqrt(3*6^2 + 13)= sqrt(121) = 11.
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CROSSREFS
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Cf. A077238 (even and odd parts).
Adjacent sequences: A077233 A077234 A077235 this_sequence A077237 A077238 A077239
Sequence in context: A106269 A126758 A050911 this_sequence A121096 A047091 A121092
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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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