0,3

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Math. Mag., vol. 67, no. 5, p. 339, Dec '94.

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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.

S. Alejandre, Legend of Towers of Hanoi

All 23 listed terms satisfy a(n) = 2a(n-1) + 2a(n-2) + 3 - John W. Layman (layman(AT)math.vt.edu).

a(n) = (1/(2*s3))*((1+s3)^(n+1)-(1-s3)^(n+1))-1 where s3 = sqrt(3).

G.f.: x(1+2x)/(1-3x+2x^3); a(n)=((sqrt(3)+1)^(n+1)+(sqrt(3)-1)^(n+1)*(-1)^n)*sqrt(3)/6-1; - Paul Barry (pbarry(AT)wit.ie), Sep 05 2006

A005665:=z*(1+2*z)/(z-1)/(2*z**2+2*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]

Cf. A007664, A007665.

Adjacent sequences: A005662 A005663 A005664 this_sequence A005666 A005667 A005668

Sequence in context: A053731 A111295 A032193 this_sequence A025471 A064453 A059251

nonn,nice

njas