MathDB

Let

n

be a positive integer. Denote

M = \{(x, y)|x, y \text{ are integers }, 1 \leq x, y \leq n\}

. Define function

f

M

with the following properties: a.)

f(x, y)

takes non-negative integer value; b.)

\sum^n_{y=1} f(x, y) = n - 1

for 1 \eq x \leq n; c.) If

f(x_1, y_1)f(x2, y2) > 0

, then

(x_1 - x_2)(y_1 - y_2) \geq 0.

Find

N(n)

, the number of functions

f

that satisfy all the conditions. Give the explicit value of

N(4)

Problem Statement