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Search: id:A049660
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| 0, 1, 18, 323, 5796, 104005, 1866294, 33489287, 600940872, 10783446409, 193501094490, 3472236254411, 62306751484908, 1118049290473933, 20062580477045886, 360008399296352015, 6460088606857290384
(list; graph; listen)
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OFFSET
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0,3
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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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G.f.: x/(1-18*x+x^2).
a(n) ~ (1/40)*sqrt(5)*(sqrt(5) + 2)^(2*n) - Joe Keane (jgk(AT)jgk.org), May 15 2002
For all elements x of the sequence, 80*x^2 + 1 is a square. Lim. n-> Inf. a(n)/a(n-1) = 8*phi + 5 = 9 + 4*Sqrt(5). - Gregory V. Richardson (omomom(AT)hotmail.com), Oct 14 2002
a(n) = S(n-1, 18) with S(n, x) := U(n, x/2), Chebyshev's polynomials of the second kind. S(-1, x) := 0. See A049310.
a(n) = (((9+4*sqrt(5))^n - (9-4*sqrt(5))^n))/(8*sqrt(5)).
a(n) = sqrt((A023039(n)^2 - 1)/80) (cf. Richardson comment).
a(n) = 18*a(n-1) - a(n-2) - Gregory V. Richardson (omomom(AT)hotmail.com), Oct 14 2002
a(n) = 17*(a(n-1)+a(n-2))-a(n-3), a(n) = 19*(a(n-1)-a(n-2))+a(n-3). a(n)=18*a(n-1)-a(n-2). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 26 2007
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MAPLE
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with (combinat):seq(fibonacci(2*n, 4)/4, n=0..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 20 2008
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MATHEMATICA
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lst={}; Do[AppendTo[lst, GegenbauerC[n, 1, 9]], {n, 0, 8^2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]
s = 0; lst = {s}; Do[s += Fibonacci[n, 4]; AppendTo[lst, s], {n, 1, 31, 2}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 14 2009]
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PROGRAM
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(Mupad) numlib::fibonacci(6*n)/8 $ n = 0..25; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2008
sage: [lucas_number1(n, 18, 1) for n in xrange(0, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008
(Other) sage: [fibonacci(6*n)/8 for n in xrange(0, 17)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 15 2009]
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CROSSREFS
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Bisection of A001076 divided by 4
A column of array A028412.
A134492 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 15 2009]
Sequence in context: A097831 A091045 A158532 this_sequence A001027 A041145 A041614
Adjacent sequences: A049657 A049658 A049659 this_sequence A049661 A049662 A049663
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 20 2000
Chebyshev and other comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 2002
More terms from Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008
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