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 A063683 Integers formed from the reduced residue sets of even numbers and Fibonacci numbers. 2

%I

%S 1,3,6,21,50,108,364,987,1938,6150,17622,34776,121160,306852,549000,

%T 2178309,5701290,11197764,39083988,93031050,191708244,697884066,

%U 1836283246,3605645232,11442062750,32888033880,64700678454

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

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

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

%e 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.

%p 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

%Y Cf. A054432, A054433, A050611.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 31 2001

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Last modified June 18 20:04 EDT 2021. Contains 345121 sequences. (Running on oeis4.)