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).

2, 1, 34, 24, 716, 14, 13784, 376, 7624, 236, 4842784, 276, 90305216, 4264, 69136, 121376, 31362601216, 5624, 584397750784, 93776, 23235136, 1463264, 202903086454784, 111376, 5280370789376, 27244736, 271771738624

Offset

1,1

Links

Table of n, a(n) for n=1..27.

Formula

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);

Example

F(12)=a(1)*a(2)*a(3)*a(4)*a(6)*a(12)=2*1*34*24*14*276=6306048
F(9)=a(2)*a(6)*a(18)= 1*14*5624=78736
L(12)=a(8)*a(24)=376*111376=41877376
L(21)=a(1)*a(3)*a(7)*a(21)=2*34*13784*23235136=21778571794432

Maple

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);

Crossrefs

Cf. A083102, A127261.

Sequence in context: A113465 A113456 A205445 * A038022 A173838 A038021

Adjacent sequences: A127605 A127606 A127607 * A127609 A127610 A127611

Keyword

nonn

Author

Miklos Kristof, Apr 03 2007

Status

approved