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A215746
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Numerator of Sum_{i=0..n} (-1)^i*4/(2*i + 1).
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1
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4, 8, 52, 304, 1052, 10312, 147916, 135904, 2490548, 44257352, 47028692, 1023461776, 5385020324, 15411418072, 467009482388, 13895021563328, 14442004718228, 13926277743608, 533322720625196, 516197940314096, 21831981985010836, 911392701638017048, 937558224301357108
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OFFSET
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0,1
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COMMENTS
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Denominator of the sum divides A025547(n+1), but is not always equal to it: the first exception is n = 32.
x(n) = Sum_{i=0..n} (-1)^i*4/(2*i+1) very slowly converges to Pi, with x(n) > Pi when n is even and x(n) < Pi when n is odd.
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LINKS
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EXAMPLE
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a(2) = 52 because 4 - 4/3 + 4/5 = 60/15 - 20/15 + 12/15 = 52/15.
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MAPLE
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N:= 100; # to get terms up to a[N]
T[0]:= 4;
for i from 1 to N do
T[i]:= T[i-1] + (-1)^i*4/(2*i+1);
od:
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MATHEMATICA
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Table[Numerator[Sum[(-1)^i 4/(2i + 1), {i, 0, n}]], {n, 0, 39}]
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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