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

0,3

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.

Prog

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

Crossrefs

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

Sequence in context: A269225 A217713 A047740 * A024745 A322921 A030581

Adjacent sequences: A137684 A137685 A137686 * A137688 A137689 A137690

Keyword

easy,nonn

Author

M. F. Hasler, Feb 06 2008

Status

approved