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%I #3 Mar 30 2012 18:36:39
%S 1,1,8,29,115,452,1779,7001,27552,108429,426715,1679308,6608803,
%T 26008497,102354680,402809917,1585231171,6238570004,24551470099,
%U 96620649225,380244026896,1496424637485,5889077900715,23176067575964
%N a(n) equals the square of the n-th partial sum added to twice the n-th partial sum of the squares, divided by a(n-1), for all n>=1, with a(0)=1, a(1)=1.
%F a(n)=4a(n-1)-a(n-3) for n>3; G.f.: A(x)=(1-3x+4x^2-2x^3)/(1-4x+x^3).
%o (PARI) a(0)=1; a(1)=1; for(n=2,30, a(n)=(sum(k=0,n-1,a(k))^2 + 2*sum(k=0,n-1,a(k)^2))/a(n-1))
%Y Cf. A088132.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Sep 19 2003