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A077250
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Bisection (odd part) of Chebyshev sequence with Diophantine property.
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5
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11, 103, 1019, 10087, 99851, 988423, 9784379, 96855367, 958769291, 9490837543, 93949606139, 930005223847, 9206102632331, 91131021099463, 902104108362299, 8929910062523527, 88396996516872971, 875040055106206183, 8662003554545188859, 85744995490345682407
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n)^2 - 24*b(n)^2 = 25, with the companion sequence b(n)= A077249(n).
The even part is A077409(n) with Diophantine companion A077251(n).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (10,-1).
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n)= 10*a(n-1)- a(n-2), a(-1) := 7, a(0)=11.
a(n)= 2*T(n+1, 5)+T(n, 5), with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 5)= A001079(n).
a(n)= sqrt(25 + 24*A077249(n)^2).
G.f.: (11-7*x)/(1-10*x+x^2).
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EXAMPLE
| 103 = a(1) = sqrt(24*A077249(1)^2 + 25) = sqrt(24*21^2 + 25) = sqrt(10609) = 103.
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MATHEMATICA
| CoefficientList[Series[(11 - 7 z)/(z^2 - 10 z + 1), {z, 0, 200}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)
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PROG
| (PARI) a(n)= 2*polchebyshev(n+1, 1, 5)+polchebyshev(n, 1, 5) \\ Charles R Greathouse IV, Jun 11 2011
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CROSSREFS
| Sequence in context: A141915 A016133 A155594 * A173851 A158470 A163933
Adjacent sequences: A077247 A077248 A077249 * A077251 A077252 A077253
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 2002
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