0,3

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

F. R. Bernhart, Topics in Graph Theory Related to the Five Color Conjecture. Ph.D. Dissertation, Kansas State Univ., 1974.

G. D. Birkhoff, D. C. Lewis, Chromatic polynomials. Trans. Amer. Math. Soc. 60, (1946). 355-451.

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.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

G.f.: (1 - 2 x ) / ( 1 - x^2 ) ( 1 - 3 x ).

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

A006342:=-(-1+2*z)/(z-1)/(3*z-1)/(z+1); [Conjectured by S. Plouffe in his 1992 dissertation.]

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

Sequence in context: A145453 A034730 A095127 this_sequence A135831 A015796 A034717

Adjacent sequences: A006339 A006340 A006341 this_sequence A006343 A006344 A006345

nonn

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)