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Search: id:A057076
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| A057076 |
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A Chebyshev or generalized Fibonacci sequence. |
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+0
4
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| 2, 11, 119, 1298, 14159, 154451, 1684802, 18378371, 200477279, 2186871698, 23855111399, 260219353691, 2838557779202, 30963916217531, 337764520613639, 3684445810532498, 40191139395243839, 438418087537149731
(list; graph; listen)
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OFFSET
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0,1
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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 recurrences a(n) = k*a(n - 1) +/- a(n - 2)
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n) = S(n, 11) - S(n-2, 11) = 2*T(n, 11/2) with S(n, x) := U(n, x/2), S(-1, x) := 0, S(-2, x) := -1. S(n, 11)=A004190(n). U-, resp. T-, are Chebyshev's polynomials of the second, resp. first, case. See A049310 and A053120.
G.f.: (2-11x)/(1-11x+x^2).
a(n)=a(-n). - Michael Somos, Apr 25 2003
a(n) = ap^n + am^n, with ap := (11+sqrt(117))/2 and am := (11-sqrt(117))/2.
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MATHEMATICA
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a[0] = 2; a[1] = 11; a[n_] := 11a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 17}] (from Robert G. Wilson v Jan 30 2004)
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PROGRAM
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(PARI) a(n)=subst(poltchebi(n), x, 11/2)*2
sage: [lucas_number2(n, 11, 1) for n in range(27)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008
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CROSSREFS
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a(n)=sqrt(4+117*A004190(n-1)^2), n>=1.
Sequence in context: A069574 A090534 A130222 this_sequence A118794 A155928 A001946
Adjacent sequences: A057073 A057074 A057075 this_sequence A057077 A057078 A057079
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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), Oct 31 2002
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