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Search: id:A077421
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| A077421 |
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Chebyshev sequence U(n,11)=S(n,22) with Diophantine property. |
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+0
3
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| 1, 22, 483, 10604, 232805, 5111106, 112211527, 2463542488, 54085723209, 1187422368110, 26069206375211, 572335117886532, 12565303387128493, 275864339398940314, 6056450163389558415, 132966039255171344816
(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 - 30*(2*a(n))^2 = 1 with the companion sequence b(n)=A077422(n+1).
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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)=22*a(n-1) - a(n-1), a(-1) := 0, a(0)=1.
a(n)= S(n, 22) 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 := 11+2*sqrt(30) and am := 11-2*sqrt(30).
a(n)= sum(((-1)^k)*binomial(n-k, k)*22^(n-2*k), k=0..floor(n/2)).
a(n)=sqrt((A077422(n+1)^2-1)/30)/2.
G.f.: 1/(1-22*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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MATHEMATICA
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lst={}; Do[AppendTo[lst, GegenbauerC[n, 1, 11]], {n, 0, 8^2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]
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PROGRAM
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sage: [lucas_number1(n, 22, 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: A036905 A139228 A158535 this_sequence A009966 A041221 A041926
Adjacent sequences: A077418 A077419 A077420 this_sequence A077422 A077423 A077424
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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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