cp's OEIS Frontend

A127608 Sequence arising from the factorization of F(n) = A083102(n-1) and L(n) = A127261. F(0) = 0, F(1) = 1, F(n) = 2*F(n-1)+10*F(n-2), L(0) = 2, L(1) = 2, L(n) = 2*L(n-1)+10*L(n-2).

%I A127608 #3 Mar 31 2012 14:39:58
%S A127608 2,1,34,24,716,14,13784,376,7624,236,4842784,276,90305216,4264,69136,
%T A127608 121376,31362601216,5624,584397750784,93776,23235136,1463264,
%U A127608 202903086454784,111376,5280370789376,27244736,271771738624
%N A127608 Sequence arising from the factorization of F(n) = A083102(n-1) and L(n) = A127261. F(0) = 0, F(1) = 1, F(n) = 2*F(n-1)+10*F(n-2), L(0) = 2, L(1) = 2, L(n) = 2*L(n-1)+10*L(n-2).
%F A127608 a(n)= (sqrt(11)-1)^degree(cyclotomic(n,x),x)*cyclotomic(n,(6+sqrt(11)/5) L(n)=10*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 A127608 F(12)=a(1)*a(2)*a(3)*a(4)*a(6)*a(12)=2*1*34*24*14*276=6306048
%e A127608 F(9)=a(2)*a(6)*a(18)= 1*14*5624=78736
%e A127608 L(12)=a(8)*a(24)=376*111376=41877376
%e A127608 L(21)=a(1)*a(3)*a(7)*a(21)=2*34*13784*23235136=21778571794432
%p A127608 with(numtheory): a[1]:=2:a[2]:=1:for n from 3 to 60 do a[n]:=round(evalf((sqrt(11)-1)^degree(cyclotomic(n, x), x) *cyclotomic(n, (6+sqrt(11))/5), 30)) od: seq(a[n], n=1..60);
%Y A127608 Cf. A083102, A127261.
%K A127608 nonn
%O A127608 1,1
%A A127608 _Miklos Kristof_, Apr 03 2007