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

Author

Antti Karttunen, Jul 31 2001

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A054432, A054433, A050611.

Programs

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

Formula

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