OFFSET
0,2
COMMENTS
The integral is 1/4^n - 1/(3*2^(3n-1)). - R. J. Mathar, Nov 24 2008
LINKS
FORMULA
a(n) = 3*6^n - 2*3^n. - R. J. Mathar, Nov 24 2008
From Philippe Deléham, Nov 26 2008: (Start)
a(n) = 9*a(n-1) - 18*a(n-2), n > 1; a(0)=1, a(1)=12.
G.f.: (1+3*x)/(1-9*x+18*x^2). (End)
EXAMPLE
For n=3, Integral_{x=0..1/(4^n)} (1 - sqrt(x)) dx = 594/41472, and b(3) = 3*24^3 = 41472, so a(3) = (594/41472)*41472 = 594.
MATHEMATICA
Table[3*6^n-2*3^n, {n, 0, 20}] (* or *) LinearRecurrence[{9, -18}, {1, 12}, 30] (* Harvey P. Dale, Jan 23 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)excite.com), May 18 2004
EXTENSIONS
Changed offset to 0. Adapted definition to the fact that these are not reduced numerators of the integral. - R. J. Mathar, Nov 24 2008
STATUS
approved