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Search: id:A063683
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| A063683 |
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Integers formed from the reduced residue sets of even numbers and Fibonacci numbers. |
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+0
2
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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a(2n) = L(2n)*a(n), where L(2n) is the 2nth Lucas number = A000032[2n]
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FORMULA
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a(n) = Sum_{i | gcd(i, 2n)=1} Fib(i) (where Fib(i) = A000045[i])
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EXAMPLE
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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.
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MAPLE
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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
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CROSSREFS
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Cf. A054432, A054433, A050611.
Sequence in context: A094282 A124493 A136331 this_sequence A098511 A112520 A054878
Adjacent sequences: A063680 A063681 A063682 this_sequence A063684 A063685 A063686
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Jul 31 2001
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