1,2

Numbers n of the form n = y^2 = 3*x^2 - 3*x + 1.

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.

M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 19.

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.

Sociedad Magic Penny Patagonia, Leonardo en Patagonia

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

a(n) = 194*a(n-1) - a(n-2) - 24, a(1)=1, a(2)=169 - James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000

a(n)=A001570(n)^2.

a(n)=(1/8)+(7/16)*[97-56*sqrt(3)]^n+(7/16)*[97+56*sqrt(3)]^n-(1/4)*[97-56*sqrt(3)]^n*sqrt(3) +(1/4)*sqrt(3)*[97+56*sqrt(3)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Sep 26 2008]

A006051:=-(1-26*z+z**2)/(z-1)/(z**2-194*z+1); [Conjectured by S. Plouffe in his 1992 dissertation.]

Cf. A003500. Intersection of A000290 and A003215. Values of x are given by A001922, values of y by A001570.

Sequence in context: A052066 A069297 A051477 this_sequence A069742 A069743 A135824

Adjacent sequences: A006048 A006049 A006050 this_sequence A006052 A006053 A006054

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).