%I A001571 M1928 N0762
%S A001571 0,2,9,35,132,494,1845,6887,25704,95930,358017,1336139,4986540,18610022,
%T A001571 69453549,259204175,967363152,3610248434,13473630585,50284273907,
%U A001571 187663465044,700369586270,2613814880037,9754889933879,36405744855480
%N A001571 a(0) = 0, a(1) = 2, a(n) = 4a(n-1) - a(n-2) + 1.
%C A001571 Second member of the Diophantine pair (m,k) that solves 3(m^2+m)=k^2+k: 
               a(n)=k. - Bruce Corrigan (scentman(AT)myfamily.com), Nov 04 2002
%D A001571 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001571 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001571 V. Thebault, Consecutive cubes with difference a square, Amer. Math. 
               Monthly, 56 (1949), 174-175.
%H A001571 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 A001571 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 A001571 a(n)=(A001834(n)-1)/2.
%F A001571 a(n)=-(1/2)-(1/4)*sqrt(3)*[2-sqrt(3)]^n+(1/4)*sqrt(3)*[2+sqrt(3)]^n+(1/
               4)*[2-sqrt(3)]^n+(1/4) *[2+sqrt(3)]^n, with n>=0 [From Paolo P. Lava 
               (ppl(AT)spl.at), Jul 31 2008]
%p A001571 A001571:=z*(-2+z)/(-1+z)/(z**2-4*z+1); [Conjectured by S. Plouffe in 
               his 1992 dissertation.]
%t A001571 a[0] = 0; a[1] = 2; a[n_] := a[n] = 4a[n - 1] - a[n - 2] + 1; Table[ 
               a[n], {n, 0, 24}] (from Robert G. Wilson v Apr 24 2004)
%Y A001571 Sequence in context: A140217 A032601 A083141 this_sequence A092431 A147762 
               A077837
%Y A001571 Adjacent sequences: A001568 A001569 A001570 this_sequence A001572 A001573 
               A001574
%K A001571 nonn
%O A001571 0,2
%A A001571 N. J. A. Sloane (njas(AT)research.att.com).
%E A001571 Better description from Bruce Corrigan (scentman(AT)myfamily.com), Nov 
               04 2002
%E A001571 More terms and new description from Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Apr 24 2004