|
Search: id:A159009
|
|
|
| A159009 |
|
Numerator of the integral of x^n times the Cantor function, from 0 to 1. |
|
+0
2
|
|
| 1, 5, 11, 233, 97, 36377, 10637, 8885119, 18040327, 107868664309, 19821442673, 2657527033463249, 412093696402361, 28353905269136197727, 57058882710461852501, 30872757660805358101602571
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
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: A036932 A162252 A006572 this_sequence A139187 A156330 A056253
Adjacent sequences: A159006 A159007 A159008 this_sequence A159010 A159011 A159012
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
Simon Tatham (anakin(AT)pobox.com), Apr 02 2009
|
|
|
Search completed in 0.002 seconds
|
