

A094064


Sequences has the properties shown in the Comments lines.


1



2, 1, 5, 4, 3, 10, 9, 8, 7, 6, 17, 16, 15, 14, 13, 12, 11, 26, 25, 24, 23, 22, 21, 20, 19, 18, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 82
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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), 463470; Zentralblatt 12,270.
Lajos Pinter, On monotone subsequences, Math. Gaz., 88 (#511, 2004), 110111.


FORMULA

G.f. (3 + 5*x^2 + 4*x*Sum_{n>=2} n*x^(n^2))/(1x)  1/(1x)^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+2i
od od:
seq(A[i], i=0..100); # Robert Israel, Jan 13 2016


CROSSREFS

Sequence in context: A280513 A185023 A061579 * A159930 A058344 A010582
Adjacent sequences: A094061 A094062 A094063 * A094065 A094066 A094067


KEYWORD

nonn


AUTHOR

R. K. Guy, May 01 2004


STATUS

approved



