OFFSET
0,1
COMMENTS
It contains an infinite increasing subsequence.
For each k there is a decreasing subsequence of length > k but no infinite decreasing subsequence.
For each n the first n^2 + 1 terms contain a decreasing subsequence of length n + 1 but no increasing subsequence of length n + 1.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
P. Erdõs, G. Szekeres, A combinatorial problem in geometry, Compositio Math. 2 (1935), 463-470; Zentralblatt 12,270.
Lajos Pinter, On monotone subsequences, Math. Gaz., 88 (#511, 2004), 110-111.
FORMULA
G.f. (3 + 5*x^2 + 4*x*Sum_{n>=2} n*x^(n^2))/(1-x) - 1/(1-x)^2. - Robert Israel, Jan 13 2016
MAPLE
A[0]:= 2:
A[1]:= 1:
for n from 1 to 9 do
for i from 1 to 2*n+1 do
A[n^2+i]:= (n+1)^2+2-i
od od:
seq(A[i], i=0..100); # Robert Israel, Jan 13 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
R. K. Guy, May 01 2004
STATUS
approved