A137687 a(n) = round(3 n / (2 log(n+2))), an approximation to A081399.

0, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 25, 25, 26, 26

Offset: 0

Author

M. F. Hasler, Feb 06 2008

Keywords

• easy
• nonn

Comments

It is easy to show that A081399(n) is between n/log(n) and 2n/log(n) (for n>n0), cf. [Campbell 1984]. This sequence A137687 is roughly the middle of this interval (with log(n) replaced by log(n+2) to be well-defined for all n>=0), which turns out to be a fair (and simple, increasing) approximation for A081399.

See A137686 for the (signed) difference of the two sequences.

Links

• M. F. Hasler, Table of n, a(n) for n = 0..3000.
• Douglas M. Campbell, The Computation of Catalan Numbers, Mathematics Magazine, Vol. 57, No. 4. (Sep., 1984), pp. 195-208.

Crossrefs

Cf. A000108, A001222, A081399, A120626, A137686.

Programs

PARI

A137687(n) = round(3*n/log(n+2)/2) \\ M. F. Hasler, Feb 06 2008