A SEQUENCE (X X1, 2,⋯,XM) OF M TERMS IS CALLED AN OE-SEQUENCE IF...

1.

A sequence

^{x x}

¹

^,

²

^,

^⋯

^,

^x

^m

of m terms is called an OE-sequence if the following two

conditions are satisfied:

a.

for any positive integer 1

≤ ≤ −

i

m

1

, we have

x

_i

≤

x

_i

₊

₁

;

b.

all the odd numbered terms

x

₁

,

x

₃

,

x

₅

, ...are odd integer, and all the even

numbered terms

x

₂

,

x

₄

,

x

₆

,... are even integer.

For instance, there are only 7 OE-sequences in which the largest term is at most 4,

namely, (1), (3), (1,2), (1,4), (3, 4), (1, 2, 3) and (1, 2, 3, 4).

How many OE-sequences are there in which the largest terms are at most 20?

Explain your answer.