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Search: id:A077423
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| A077423 |
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Chebyshev sequence U(n,12)=S(n,24) with diophantine property. |
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+0
2
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| 1, 24, 575, 13776, 330049, 7907400, 189447551, 4538833824, 108742564225, 2605282707576, 62418042417599, 1495427735314800, 35827847605137601, 858372914787987624, 20565122107306565375, 492704557660569581376
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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b(n)^2 - 143*a(n)^2 = 1 with the companion sequence b(n)=A077424(n+1).
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LINKS
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Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
Zerinvary Lajos, Sage Notebooks
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FORMULA
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a(n)=24*a(n-1) - a(n-2), a(-1) := 0, a(0)=1.
a(n)= S(n, 24) with S(n, x) := U(n, x/2) Chebyshev's polynomials of the 2nd kind. See A049310.
a(n)= (ap^(n+1) - am^(n+1))/(ap - am) with ap := 12+sqrt(143) and am := 12-sqrt(143).
a(n)= sum(((-1)^k)*binomial(n-k, k)*24^(n-2*k), k=0..floor(n/2)).
a(n)=sqrt((A077424(n+1)^2 - 1)/143).
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PROGRAM
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sage: [lucas_number1(n, 24, 1) for n in xrange(1, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008
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CROSSREFS
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Sequence in context: A063816 A007110 A007109 this_sequence A059061 A009968 A041265
Adjacent sequences: A077420 A077421 A077422 this_sequence A077424 A077425 A077426
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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 29 2002
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