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Search: id:A097313
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| A097313 |
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Chebyshev polynomials of the second kind, U(n,x), evaluated at x=15. |
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+0
2
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| 0, 1, 30, 899, 26940, 807301, 24192090, 724955399, 21724469880, 651009141001, 19508549760150, 584605483663499, 17518655960144820, 524975073320681101, 15731733543660288210, 471427031236487965199, 14127079203550978667760
(list; graph; listen)
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OFFSET
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-1,3
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COMMENT
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b(n+1)^2 - 14*(4*a(n))^2 = +1, n>=-1, with b(n):=A068203(n) gives all nonnegative integer solutions of this D=224 Pell equation.
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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)= S(n, 30) = U(n, 15), n>=-1, with Chebyshev polynomials of 2nd kind. See A049310 for the triangle of S(n, x) coefficients. S(-1, x) := 0 =: U(-1, x).
G.f.: 1/(1-30*x+x^2).
a(n)= ((15+4*sqrt(14))^(n+1) - (15-4*sqrt(14))^(n+1))/(8*sqrt(14)) (Binet form).
a(n)=30*a(n-1)-a(n-2) for n>0; a(-1)=0, a(0)=1. [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, 15]], {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, 30, 1) for n in xrange(0, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2008
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CROSSREFS
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a(n) = sqrt((A068203(n+1)^2 - 1)/224), n>=-1.
Sequence in context: A001201 A007850 A158580 this_sequence A056389 A056379 A009974
Adjacent sequences: A097310 A097311 A097312 this_sequence A097314 A097315 A097316
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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_DOT_uni-karlsruhe_DOT_de), Aug 31 2004
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