AUTHOR
_Alexander Adamchuk (alex(AT)kolmogorov.com), _, Aug 16 2006
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Revision History for A121709
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NAME
Numerator of Sum/Product of first n Lucas numbers A000032[n].
DATA
1, 4, 2, 5, 13, 1, 73, 5, 7, 1, 37, 5, 1361, 1, 223, 25, 4673, 1, 24473, 25, 16019, 1, 83879, 65, 62743, 1, 20533, 65, 1505173, 1, 7881193, 85, 5158309, 1, 27009259, 425, 1400221, 1, 1446283, 2225, 69237359, 1, 51790217, 445, 1660959719, 1, 8696897999
OFFSET
1,2
COMMENTS
5 divides a(4k). a(1) = 1 and a(4k+2) = 1 for k>0.
FORMULA
a(n) = Numerator[Sum[Lucas[k],{k,1,n}]/Product[Lucas[k],{k,1,n}]], where Lucas[k] = Fibonacci[k-1] + Fibonacci[k+1].
MATHEMATICA
Table[Numerator[Sum[Fibonacci[k-1]+Fibonacci[k+1], {k, 1, n}]/Product[Fibonacci[k-1]+Fibonacci[k+1], {k, 1, n}]], {n, 1, 100}]
KEYWORD
frac,nonn
AUTHOR
Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 16 2006
STATUS
approved