MathDB

The positive integer

n

is given and for all positive integers

k

1\leq k\leq n

, denote by

a_{kn}

the number of all ordered sequences

(i_1,i_2,\ldots,i_k)

of positive integers which verify the following two conditions: a)

1\leq i_1<i_2< \cdots i_k \leq n

; b)

i_{r+1}-i_r \equiv 1 \pmod 2

, for all

r \in\{1,2,\ldots,k-1\}

. Compute the number

a(n) = \sum\limits_{k=1}^n a_{kn}

. Ioan Tomescu

Problem Statement