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A159009
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Numerator of the integral of x^n times the Cantor function, from 0 to 1.
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1
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1, 5, 11, 233, 97, 36377, 10637, 8885119, 18040327, 107868664309, 19821442673, 2657527033463249, 412093696402361, 28353905269136197727, 57058882710461852501, 30872757660805358101602571
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OFFSET
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0,2
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LINKS
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FORMULA
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I(n) = 1/(2*(n+1)) + 1/(2*3^(n+1)-1) * sum_{i=0}{n-1} (n choose i) 2^(n-i) I(i)
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EXAMPLE
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I(0) is obviously 1/2 by symmetry.
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MAPLE
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for n from 0 to 20 do CI[n] := 1/(2*(n+1)) + 1/(2*(3^(n+1)-1)) * add(binomial(n, i)*2^(n-i)*CI[i], i=0..n-1); end do;
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CROSSREFS
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A095844/A095845 give the integrals of powers of the Cantor function itself.
A159010 gives the corresponding denominators. [From Simon Tatham (anakin(AT)pobox.com), Apr 02 2009]
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KEYWORD
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frac,nonn
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AUTHOR
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Simon Tatham (anakin(AT)pobox.com), Apr 02 2009
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STATUS
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approved
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