Search: id:A028859
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%I A028859
%S A028859 1,3,8,22,60,164,448,1224,3344,9136,24960,68192,186304,
%T A028859 508992,1390592,3799168,10379520,28357376,77473792,211662336,
%U A028859 578272256,1579869184,4316282880,11792304128,32217174016
%N A028859 a(n+2) = 2 a(n+1) + 2 a(n).
%C A028859 Number of words of length n without adjacent 0's from the alphabet {0,
               1,2}. For example, a(2) counts 01,02,10,11,12,20,21,22. - Antonio 
               G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 12 2001
%C A028859 Individually, both this sequence and A002605 are convergents to 1+sqrt(3). 
               Mutually, both sequences are convergents to 2+sqrt(3) and 1+sqrt(3)/
               2.- Klaus E. Kastberg (kastberg(AT)hotkey.net.au), Nov 04 2001
%C A028859 Add a loop at two vertices of the graph C_3=K_3. A028859(n) counts walks 
               of length n+1 between these vertices. - Paul Barry (pbarry(AT)wit.ie), 
               Oct 15 2004
%C A028859 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 28 2009: 
               (Start)
%C A028859 Prefaced with a 1 as (1 + x + 3x^2 + 8x^3 + 22x^4 + ...) =
%C A028859 1 / (1 - x - 2x^2 - 3x^3 - 5x^4 - 8x^5 - 13x^6 - 21x^7 - ...). (End)
%D A028859 S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, 
               Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see 
               p. 73).
%D A028859 David Garth and Adam Gouge, Affinely Self-Generating Sets and Morphisms, 
               Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.5.
%H A028859 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A028859 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Fxtbook</a>
%H A028859 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A028859 a(n) = a(n-1) + A052945(n) = A002605(n) + A002605(n-1); generating function 
               = -(x+1)/(2*x^2+2*x-1).
%F A028859 a(n)=[(1+sqrt(3))^(n+2)-(1-sqrt(3))^(n+2)]/(4sqrt(3)). - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), Feb 01 2005
%p A028859 a[0]:=1:a[1]:=3:for n from 2 to 24 do a[n]:=2*a[n-1]+2*a[n-2] od: seq(a[n],
               n=0..24); (Deutsch)
%Y A028859 Sequence in context: A077848 A055887 A024581 this_sequence A155020 A014397 
               A048503
%Y A028859 Adjacent sequences: A028856 A028857 A028858 this_sequence A028860 A028861 
               A028862
%K A028859 nonn
%O A028859 0,2
%A A028859 N. J. A. Sloane (njas(AT)research.att.com).

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