OFFSET
0,3
COMMENTS
Previous name was: Sorting numbers (see Motzkin article for details).
Since a(n) by definition is the largest among some positive integers, whose sum is A002872(n), we always have the relation a(n) <= A002872(n); and for n > 0 the inequality is strict, since then that sum consists of more than one term. - Jörgen Backelin, Jan 13 2016
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..514
Victor Meally, Comparison of several sequences given in Motzkin's paper "Sorting numbers for cylinders...", letter to N. J. A. Sloane, N. D.
T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]
OEIS Wiki, Sorting numbers
EXAMPLE
There are three partitions of {1,2,3,4} into two (nonempty) parts, and which are invariant under the permutation (1,2)(3,4), namely {{1,2}, {3,4}}, {{1,3}, {2,4}}, and {{1,4}, {2,3}}. There are also one such partition with just one part, two with three parts, and one with four parts; but three is the largest of these amounts. Thus, a(2) = 3.
Similarly, there are ten (1,2)(3,4)(5,6) invariant partitions of {1,2,3,4,5,6} into three nonempty parts, and no larger amount into any other given number of parts, whence a(3) = 10.
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
Name changed and example added by Jörgen Backelin, Jan 13 2016
a(7)-a(8) from Sean A. Irvine, Jun 19 2016
a(9)-a(22) from Andrew Howroyd, Oct 01 2017
STATUS
approved