A063683 Integers formed from the reduced residue sets of even numbers and Fibonacci numbers.

1, 3, 6, 21, 50, 108, 364, 987, 1938, 6150, 17622, 34776, 121160, 306852, 549000, 2178309, 5701290, 11197764, 39083988, 93031050, 191708244, 697884066, 1836283246, 3605645232, 11442062750, 32888033880, 64700678454

Offset

1,2

Comments

a(2n) = L(2n)*a(n), where L(2n) is the 2n-th Lucas number = A000032(2n).

Links

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

Formula

a(n) = Sum_{i | gcd(i, 2n)=1} Fib(i) (where Fib(i) = A000045[i])

Example

The reduced residue set of 2*6 = 12 is {1,5,7,11}, thus a(6) = F_1 + F_5 + F_7 + F_11 = 108.

Maple

A063683 := [seq(A063683_as_sum(2*n), n=1..101)]; A063683_as_sum := proc(n) local i; RETURN(add((one_or_zero(igcd(n, i))*fibonacci(i)), i=1..(n-1))); end; Yours, Antti Karttunen

Crossrefs

Cf. A054432, A054433, A050611.

Sequence in context: A094282 A124493 A136331 * A200380 A354017 A151396

Adjacent sequences: A063680 A063681 A063682 * A063684 A063685 A063686

Keyword

nonn

Author

Antti Karttunen, Jul 31 2001

Status

approved