%I A006342 M3398
%S A006342 1,1,4,10,31,91,274,820,2461,7381,22144,66430,199291,597871,
%T A006342 1793614,5380840,16142521,48427561,145282684,435848050,1307544151,
%U A006342 3922632451,11767897354,35303692060,105911076181,317733228541
%N A006342 Coloring a circuit with 4 colors.
%D A006342 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006342 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A006342 F. R. Bernhart, Topics in Graph Theory Related to the Five Color Conjecture. 
               Ph.D. Dissertation, Kansas State Univ., 1974.
%D A006342 G. D. Birkhoff, D. C. Lewis, Chromatic polynomials. Trans. Amer. Math. 
               Soc. 60, (1946). 355-451.
%H A006342 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A006342 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A006342 G.f.: (1 - 2 x ) / ( 1 - x^2 ) ( 1 - 3 x ).
%F A006342 Binomial transform of A002001 (with interpolated zeros). Partial sums 
               of A054878. E.g.f.: exp(x)(3cosh(2x)+1)/4; a(n)=3*3^n/8+1/4+3(-1)^n/
               8=sum{k=0..n, (3^k+3(-1)^k)/4 }. - Paul Barry (pbarry(AT)wit.ie), 
               Sep 03 2003
%p A006342 A006342:=-(-1+2*z)/(z-1)/(3*z-1)/(z+1); [Conjectured by S. Plouffe in 
               his 1992 dissertation.]
%p A006342 a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]+3*a[n-2]-1 od: seq(a[n], 
               n=1..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 28 
               2008
%Y A006342 Sequence in context: A145453 A034730 A095127 this_sequence A135831 A015796 
               A034717
%Y A006342 Adjacent sequences: A006339 A006340 A006341 this_sequence A006343 A006344 
               A006345
%K A006342 nonn
%O A006342 0,3
%A A006342 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)