A159009 Numerator of the integral of x^n times the Cantor function, from 0 to 1.

1, 5, 11, 233, 97, 36377, 10637, 8885119, 18040327, 107868664309, 19821442673, 2657527033463249, 412093696402361, 28353905269136197727, 57058882710461852501, 30872757660805358101602571

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

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)

Example

I(0) is obviously 1/2 by symmetry.

Maple

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;

Crossrefs

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]

Sequence in context: A375161 A006572 A184934 * A230841 A139187 A266517

Adjacent sequences: A159006 A159007 A159008 * A159010 A159011 A159012

Keyword

frac,nonn

Author

Simon Tatham (anakin(AT)pobox.com), Apr 02 2009

Status

approved