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A137687 a(n) = round(3 n / (2 log(n+2))), an approximation to A081399. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 20 06:36 EDT 2019. Contains 326139 sequences. (Running on oeis4.)