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Search: id:A097311
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| A097311 |
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Chebyshev polynomials of the second kind, U(n,x), evaluated at x=14. |
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+0
2
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| 0, 1, 28, 783, 21896, 612305, 17122644, 478821727, 13389885712, 374437978209, 10470873504140, 292810020137711, 8188209690351768, 228977061309711793, 6403169506981578436, 179059769134174484415, 5007270366249903985184
(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)^2 - 195*a(n)^2 = +1 with b(n):=A097310(n) gives all nonnegative integer solutions of this Pell equation.
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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)= S(n, 28) = U(n, 14), n>=-1, with Chebyshev polynomials of the second kind. See A049310 for the triangle of S(n, x) coefficients. S(-1, x) := 0 =: U(-1, x).
G.f.: 1/(1-28*x+x^2).
a(n)= ((14+sqrt(195))^(n+1) - (14-sqrt(195))^(n+1))/(2*sqrt(195)), (Binet form).
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PROGRAM
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sage: [lucas_number1(n, 28, 1) for n in xrange(0, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008
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CROSSREFS
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a(n) = sqrt((A097310(n)^2 - 1)/195).
Sequence in context: A097834 A063817 A113532 this_sequence A009972 A114037 A041365
Adjacent sequences: A097308 A097309 A097310 this_sequence A097312 A097313 A097314
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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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