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A049660
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a(n)=F(6n)/8, where F=A000045 (the Fibonacci sequence).
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16
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0, 1, 18, 323, 5796, 104005, 1866294, 33489287, 600940872, 10783446409, 193501094490, 3472236254411, 62306751484908, 1118049290473933, 20062580477045886, 360008399296352015, 6460088606857290384
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| For n>=2, a(n) equals the permanent of the (n-1)X(n-1) tridiagonal matrix with 18's along the main diagonal, and i's along the superdiagonal and the subdiagonal (i is the imaginary unit). [From John M. Campbell, Jul 08 2011]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..200
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
| 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
a(n+1) = Sum_{k, 0<=k<=n} A101950(n,k)*17^k. - DELEHAM Philippe, Feb 10 2012
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MAPLE
| 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
| Fibonacci[6*Range[0, 20]]/8 (* From Harvey P. Dale, Nov 23 2011 *)
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PROG
| (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
| 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: A179121 A158532 A171323 * A207344 A207267 A207022
Adjacent sequences: A049657 A049658 A049659 * A049661 A049662 A049663
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KEYWORD
| nonn,changed
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| 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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