Problem

Source: 2004 Estonia National Olympiad Final Round grade 10 p4

Tags: lattice, Sum, combinatorics



In the beginning, number $1$ has been written to point $(0,0)$ and $0$ has been written to any other point of integral coordinates. After every second, all numbers are replaced with the sum of the numbers in four neighbouring points at the previous second. Find the sum of numbers in all points of integral coordinates after $n$ seconds.