Search: id:A006051
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%I A006051 M5409
%S A006051 1,169,32761,6355441,1232922769,239180661721,46399815451081,9001325016847969,
%T A006051 1746210653453054881,338755865444875798921,65716891685652451935769,
%U A006051 12748738231151130799740241,2473189499951633722697670961,479786014252385791072548426169
%N A006051 Square hex numbers.
%C A006051 Numbers n of the form n = y^2 = 3*x^2 - 3*x + 1.
%D A006051 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006051 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 A006051 M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, 
               NY, 1988, p. 19.
%H A006051 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 A006051 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.
%H A006051 Sociedad Magic Penny Patagonia, <a href="http://www.magicpenny.org/engteorema.htm">
               Leonardo en Patagonia</a>
%H A006051 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HexNumber.html">Link to a section of The World of Mathematics.</a>
%F A006051 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
%F A006051 a(n)=A001570(n)^2.
%F A006051 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]
%p A006051 A006051:=-(1-26*z+z**2)/(z-1)/(z**2-194*z+1); [Conjectured by S. Plouffe 
               in his 1992 dissertation.]
%Y A006051 Cf. A003500. Intersection of A000290 and A003215. Values of x are given 
               by A001922, values of y by A001570.
%Y A006051 Sequence in context: A052066 A069297 A051477 this_sequence A069742 A069743 
               A135824
%Y A006051 Adjacent sequences: A006048 A006049 A006050 this_sequence A006052 A006053 
               A006054
%K A006051 nonn,easy
%O A006051 1,2
%A A006051 N. J. A. Sloane (njas(AT)research.att.com).

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