MathDB

Let

a_1, a_2, . . ., a_n

be a finite sequence of

0

and

1

. Under any two consecutive terms of this sequence

0

is written if the digits are equal and

1

is written otherwise. This way a new sequence of length

n -1

is obtained. By repeating this procedure

n - 1

times one obtains a triangular table of

0

and

1

. Find the maximum possible number of ones that can appear on this table

Problem Statement