Search: id:A008776
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%I A008776
%S A008776 2,6,18,54,162,486,1458,4374,13122,39366,118098,354294,1062882,3188646,
%T A008776 9565938,28697814,86093442,258280326,774840978,2324522934,6973568802,20920706406,
%U A008776 62762119218,188286357654,564859072962,1694577218886,5083731656658,15251194969974
%N A008776 Pisot sequences E(2,6), L(2,6), P(2,6), T(2,6).
%C A008776 Warning: there is a considerable overlap between this entry and the essentially 
               identical A025192. A025192 is the main entry.
%C A008776 Number of tilings of a 4 X 4n+4 rectangle into T tetrominoes.
%C A008776 Numbers n such that 3^n = n/2 mod n. Cf. A066601 3^n mod n. - Zak Seidov, 
               Aug 26 2006, Nov 20 2008
%C A008776 For n>=1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2,
               3} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3} 
               we have f(x)<>y. - Aleksandar M. Janjic and Milan R. Janjic (agnus(AT)blic.net), 
               Mar 27 2007
%C A008776 a(n)=EulerPhi[3^n] [From Artur Jasinski (grafix(AT)csl.pl), Nov 19 2008]
%C A008776 a(n) = A048473+1 = A048473+A000012. a(n) = A052919(n+1)-1. a(n) = A115099-2. 
               a(n) = A100774+2. See A007395. [From Paul Curtz (bpcrtz(AT)free.fr), 
               Jan 20 2009]
%D A008776 S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, 
               Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see 
               p. 203).
%H A008776 Franklin T. Adams-Watters, <a href="b008776.txt">Table of n, a(n) for 
               n = 0..200</a>
%H A008776 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A008776 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=170">
               Encyclopedia of Combinatorial Structures 170</a>
%H A008776 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas 
               for Some Functions on Finite Sets</a>
%H A008776 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A008776 C. Moore, <a href="http://arXiv.org/abs/math.CO/9905012">[math/9905012] 
               Some Polyomino Tilings of the Plane</a>
%F A008776 a(n) = 2*3^n; a(n) = 3a(n-1).
%F A008776 Pisot sequence E(x, y): a(0) = x, a(1) = y, a(n) = roundUp(a(n-1)^2/a(n-2)) 
               = [ a(n-1)^2/a(n-2) + 1/2 ].
%F A008776 Pisot sequence L(x, y): a(0) = x, a(1) = y, a(n) = ceiling(a(n-1)^2/a(n-2)).
%F A008776 Pisot sequence P(x, y): a(0) = x, a(1) = y, a(n) = roundDown(a(n-1)^2/
               a(n-2)) = ceiling(a(n-1)^2/a(n-2) - 1/2).
%F A008776 Pisot sequence T(x, y): a(0) = x, a(1) = y, a(n) = floor(a(n-1)^2/a(n-2)) 
               = [ a(n-1)^2/a(n-2) ].
%F A008776 G.f.: 2/(1-3x) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 08 
               2007
%F A008776 a(n)=EulerPhi[3^n] [From Artur Jasinski (grafix(AT)csl.pl), Nov 19 2008]
%F A008776 E.g.f.: 2*e^(3*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), 
               Jan 15 2009]
%p A008776 with(finance):seq(futurevalue(2,2,n), n=0..27);# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
%p A008776 with(finance):seq(futurevalue(6,2,n), n=-1..26);# [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
%t A008776 Table[EulerPhi[3^n], {n, 0, 100}] [From Artur Jasinski (grafix(AT)csl.pl), 
               Nov 19 2008]
%Y A008776 Apart from initial term, same as A025192. Cf. A080643.
%Y A008776 Sequence in context: A072852 A072853 A025192 this_sequence A134635 A114464 
               A062415
%Y A008776 Adjacent sequences: A008773 A008774 A008775 this_sequence A008777 A008778 
               A008779
%K A008776 easy,nonn
%O A008776 0,1
%A A008776 N. J. A. Sloane (njas(AT)research.att.com), David W. Wilson (davidwwilson(AT)comcast.net)

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