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Search: id:A077412
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| A077412 |
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Chebyshev U(n,x) polynomial evaluated at x=8. |
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+0
7
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| 1, 16, 255, 4064, 64769, 1032240, 16451071, 262184896, 4178507265, 66593931344, 1061324394239, 16914596376480, 269572217629441, 4296240885694576, 68470281953483775, 1091228270370045824, 17391182043967249409
(list; graph; listen)
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OFFSET
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0,2
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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) = 16*a(n-1) - a(n-2), n>=1, a(-1)=0, a(0)=1.
a(n) = S(n, 16) with S(n, x) := U(n, x/2), Chebyshev's polynomials of the second kind. See A049310.
G.f.: 1/(1-16*x+x^2).
a(n) = (((8+3*sqrt(7))^(n+1) - (8-3*sqrt(7))^(n+1)))/(6*sqrt(7)).
a(n) = sqrt(A001081(n+1)^2-1)/63).
a(n+1)=16a(n)- a(n-1) a(1)=1 , a(2)=16 [From Sture Sjoestedt (sture.sjostedt(AT)spray.se), May 31 2009]
a(n)=((8+Sqrt(63))^n -(8-Sqrt(63)^n)/(2*Sqrt(63)) [From Sture Sjoestedt (sture.sjostedt(AT)spray.se), May 31 2009]
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MATHEMATICA
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lst={}; Do[AppendTo[lst, GegenbauerC[n, 1, 8]], {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, 16, 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: A138460 A110394 A158531 this_sequence A135554 A017570 A016744
Adjacent sequences: A077409 A077410 A077411 this_sequence A077413 A077414 A077415
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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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