MathDB

Find the number of sequences of

0, 1

with length

n

satisfying both of the following properties:
[*] There exists a simple polygon such that its

i

-th angle is less than

180

degrees if and only if the

i

-th element of the sequence is

1

. [*] There exists a convex polygon such that its

i

-th angle is less than

90

degrees if and only if the

i

-th element of the sequence is

1

4