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A063683 Integers formed from the reduced residue sets of even numbers and Fibonacci numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A151396 A148604

Adjacent sequences:  A063680 A063681 A063682 * A063684 A063685 A063686

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jul 31 2001

STATUS

approved

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Last modified December 13 14:58 EST 2017. Contains 295958 sequences.