Search: id:A007655
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%I A007655 M4948
%S A007655 0,1,14,195,2716,37829,526890,7338631,102213944,1423656585,
%T A007655 19828978246,276182038859,3846719565780,53577891882061,
%U A007655 746243766783074,10393834843080975,144767444036350576
%N A007655 Standard deviation of A007654.
%C A007655 a(n)=A001353(2n)/4. a(n) corresponds also to one-sixth the area of Fleenor-Heronian 
               triangle with middle side A003500(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Jul 15 2002
%C A007655 a(n) give all (nontrivial, integer) solutions of Pell equation b(n+1)^2 
               - 48*a(n+1)^2 = +1 with b(n+1)=A011943(n), n>=0.
%C A007655 Number of units of a(n) belongs to a periodic sequence: 0, 1, 4, 5, 6, 
               9.We conclude that a(n) and a(n+6) have the same number of units. 
               [From Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 05 2009]
%D A007655 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007655 D. A. Benaron, personal communication.
%D A007655 E. K. Lloyd (E.K.Lloyd(AT)maths.soton.ac.uk), "The standard deviation 
               of 1, 2, .., n, Pell's equation and rational triangles", preprint.
%H A007655 T. D. Noe, <a href="b007655.txt">Table of n, a(n) for n=1..100</a>
%H A007655 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A007655 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A007655 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A007655 a(n) = 14*a(n-1) - a(n-2). G.f.: (x^2)/(1-14*x+x^2).
%F A007655 a(n+1) ~ 1/24*sqrt(3)*(2 + sqrt(3))^(2*n) - Joe Keane (jgk(AT)jgk.org), 
               May 15 2002
%F A007655 a(n+1) = S(n-1, 14), n>=0, with S(n, x) := U(n, x/2) Chebyshev's polynomials 
               of the second kind. S(-1, x) := 0. See A049310.
%F A007655 a(n+1) = ((7+4*sqrt(3))^n - (7-4*sqrt(3))^n)/(8*sqrt(3)).
%F A007655 a(n+1) = sqrt((A011943(n)^2 - 1)/48), n>=0.
%F A007655 Chebyshev's polynomials U(n-2, x) evaluated at x=7.
%F A007655 4*a(n+1) + A046184(n) = A055793(n+2) + A098301(n+1) 4*a(n+1) + A098301(n+1) 
               + A055793(n+2) = A046184(n+1) (4*a(n+1))^2 = A098301(2n+1) (conjectures) 
               - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Nov 
               02 2004
%F A007655 (4*a(n))^2 = A103974(n)^2 - A011922(n-1)^2. - Paul D. Hanna (pauldhanna(AT)juno.com), 
               Mar 06 2005
%F A007655 a(n) = 13*(a(n-1)+a(n-2))-a(n-3), a(n) = 15*(a(n-1)-a(n-2))+a(n-3). a(n)=14*a(n-1)-a(n-2). 
               - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 26 2007
%t A007655 lst={};Do[AppendTo[lst, GegenbauerC[n, 1, 7]], {n, 0, 8^2}];lst [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008]
%o A007655 sage: [lucas_number1(n,14,1) for n in xrange(0,20)] - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 25 2008
%Y A007655 Cf. A001353, A003500.
%Y A007655 Cf. A011945, A067900.
%Y A007655 Cf. A103974, A011922.
%Y A007655 Sequence in context: A055759 A086946 A158530 this_sequence A001023 A067221 
               A072533
%Y A007655 Adjacent sequences: A007652 A007653 A007654 this_sequence A007656 A007657 
               A007658
%K A007655 nonn,easy
%O A007655 1,3
%A A007655 N. J. A. Sloane (njas(AT)research.att.com).
%E A007655 Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), 
               Nov 08 2002

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