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A127609 Sequence arising from the factorization of F(n)= A091914(n-1) and L(n)= A127262. F(0)=0, F(1)=1, F(n)=2*F(n-1)+12*F(n-2), L(0)=2, L(1)=2, L(n)=2*L(n-1)+12*L(n-2).

%I A127609 #3 Mar 31 2012 14:39:58
%S A127609 2,1,40,28,976,16,21568,496,11584,304,9868288,352,209588224,6208,
%T A127609 113920,204544,94347526144,8128,2001299832832,153856,49205248,2747392,
%U A127609 900422667599872,183808,19568631218176,58200064,874289299456,69013504
%N A127609 Sequence arising from the factorization of F(n)= A091914(n-1) and L(n)= A127262. F(0)=0, F(1)=1, F(n)=2*F(n-1)+12*F(n-2), L(0)=2, L(1)=2, L(n)=2*L(n-1)+12*L(n-2).
%F A127609 a(n)= (sqrt(13)-1)^degree(cyclotomic(n,x),x)*cyclotomic(n,(7+sqrt(13)/6) L(n)=12*F(n-1)+F(n+1) F(2n)=Product(d|2n) a(d), F(2n+1)=Product(d|2n+1) a(2d). L(2n+1)=Product(d|2n+1, a(d)), for k>0: L(2^k*(2n+1))=Product(d|2n+1, a(2^(k+1)*d)). for odd prime p, a(p)=L(p)/2, a(2p)=f(p) a(1)=2, a(2)=1; a(2^(k+1))=L(2^k);
%e A127609 F(12)=a(1)*a(2)*a(3)*a(4)*a(6)*a(12)=2*1*40*28*16*352=12615680
%e A127609 F(9)=a(2)*a(6)*a(18)= 1*16*8128=130048
%e A127609 L(12)=a(8)*a(24)=496*183808=91168768
%e A127609 L(21)=a(1)*a(3)*a(7)*a(21)=2*40*21568*49205248=84900703109120
%p A127609 with(numtheory): a[1]:=2:a[2]:=1:for n from 3 to 60 do a[n]:=round(evalf((sqrt(13)-1)^degree(cyclotomic(n, x), x) *cyclotomic(n, (7+sqrt(13))/6), 30)) od: seq(a[n], n=1..60);
%Y A127609 Cf. A091914, A127262.
%K A127609 nonn
%O A127609 1,1
%A A127609 _Miklos Kristof_, Apr 03 2007