IMO 1988 LL MEX61

Origin: MEX

Problem

Prove that the numbers A, B, and C are equal, where we define A as the number of ways that we can cover a 2 \times n rectangle with 2 \times 1 rectangles, B as the number of sequences of ones and twos that add up to n, and C as .
m  +
m+1 

• \cdot \cdot \cdot +
  2m 2m  if n = 2m,
  m+1 

m+2 

• \cdot \cdot \cdot +
  2m+1 2m+1  if n = 2m + 1.