A093801 a(n) = b(n)*Integral_{x=0..1/(4^n)} (1 - sqrt(x)) dx, where b(n) = 3*24^n.

1, 12, 90, 594, 3726, 22842, 138510, 835434, 5025726, 30193722, 181280430, 1088036874, 6529284126, 39178893402, 235082926350, 1410526255914, 8463243628926, 50779720053882, 304679095164270, 1828076895508554, 10968468346620126

Offset

0,2

Comments

The integral is 1/4^n - 1/(3*2^(3n-1)). - R. J. Mathar, Nov 24 2008

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (9,-18)

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

Sequence in context: A090749 A130592 A002544 * A273099 A249979 A231512

Adjacent sequences: A093798 A093799 A093800 * A093802 A093803 A093804

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