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A128500
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Numerators of partial sums for a series for Pi/(3*sqrt(3)).
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2
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1, 1, 1, 3, 11, 11, 97, 159, 159, 187, 1777, 1777, 26181, 23321, 23321, 51647, 797919, 797919, 16521821, 15228529, 15228529, 16404249, 351431887, 351431887, 1876142299, 1761735699, 1761735699, 1867970399, 51196569971, 51196569971
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OFFSET
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0,4
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COMMENTS
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The denominators are given in A128501.
The limit n -> infinity of the rationals r(n) defined below is Pi/(3*sqrt(3).
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LINKS
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FORMULA
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a(n)=numerator(r(n)) with the rationals r(n):=sum(((-1)^k)*S(k,1)/(k+1),k=0..n) with Chebyshev's S-Polynomials S(k,1)=[1,1,0,-1,-1,0] periodic sequence with period 6. See A010892.
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EXAMPLE
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Rationals: [1, 1/2, 1/2, 3/4, 11/20, 11/20, 97/140, 159/280, 159/280, 187/280,...]
Pi/(3*sqrt(3))=+1/1 -1/2 +1/4 -1/5 +1/7 -1/8 +1/10 -1/11 +1/13 -+
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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