Half Integers

Author: mathforces
Problem has been solved: 2 times

Русский язык | English Language

Let $X_n$ be the set of points $(\frac{a}{2}, \frac{b}{2})$ such that $|a| \leq b \leq 2n$, where $a$ and $b$ are odd integers. Let $K_n$ be the number of graphs $G$ with vertices at points $X_n$ such that in the graph $G$:
• no cycles
• the length of any edge is $1$
• for any path $P = (p_1, ..., p_m)$ of the graph $G$, at least one of the points $p_1$ and $p_m$ has the smallest value of the $y$ -coordinate among the points of the path $P$. Moreover, it is possible that several points have the smallest value of the $y$ -coordinate.
Find the hundredth smallest positive integer number $t$ such that $K_{3t}$ has the last digit 4.