cp's OEIS Frontend

A127259 Sequence arising from the factorization of F(n)=A002605 and L(n)=A080040 F(0)=0, F(1)=1, F(n)=2*F(n-1)+2*F(n-2), L(0)=2, L(1)=2, L(n)=2*L(n-1)+2*L(n-2).

%I A127259 #4 Mar 31 2012 14:39:58
%S A127259 2,1,10,8,76,6,568,56,424,44,31648,52,236224,328,2320,3104,13160704,
%T A127259 408,98232832,2896,129088,18272,5472827392,3088,537496576,136384,
%U A127259 71911936,161344,2275853910016,3856,16987204845568
%N A127259 Sequence arising from the factorization of F(n)=A002605 and L(n)=A080040 F(0)=0, F(1)=1, F(n)=2*F(n-1)+2*F(n-2), L(0)=2, L(1)=2, L(n)=2*L(n-1)+2*L(n-2).
%F A127259 (sqrt(3)-1)^degree(cyclotomic(n,x),x)*cyclotomic(n,2+sqrt(3)) L(n)=2*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 A127259 F(12)=a(1)*a(2)*a(3)*a(4)*a(6)*a(12)=2*1*10*8*6*52=49920
%e A127259 F(9)=a(2)*a(6)*a(18)= 1*6*408=2448
%e A127259 L(12)=a(8)*a(24)=56*3088=172928
%e A127259 L(21)=a(1)*a(3)*a(7)*a(21)=2*10*568*129088=1466439680
%p A127259 with(numtheory): a[1]:=2:a[2]:=1:for n from 3 to 60 do a[n]:=round(evalf((sqrt(3)-1)^degree(cyclotomic(n,x),x)*cyclotomic(n,2+sqrt(3)),30)) od: seq(a[n],n=1..60);
%Y A127259 Cf. A002605, A080040.
%K A127259 nonn
%O A127259 1,1
%A A127259 _Miklos Kristof_, Mar 26 2007