Domino-and-tromino-tiling

help
, ,
1

Problem Link - [https://www.iarcs.org.in/inoi/online-study-material/topics/dp-tiling.php](https://A more complicated tiling problem)

In this edutorial there is two problem.

part-1) Some tiling problems (I understand this completely)

part-2) A more complicated tiling problem (I have doubt in this)

the recurrence relation is f(n) = f(n-1) + f(n-2) + 2g(n-2)

I have doubt in function g(n) → (covering n*2 grid using L-shaped tile)
here after using one L-shaped tile and then calling for g(n-2), i think there will be one uncovered square.

is the recurrence relation is correct.
please elaborate.

2

I got some explanation for this question but i have some doubt ;; please Help!!!

  • The Dp formula for this question is this dp[n]=dp[n-1]+dp[n-2]+ 2*(dp[n-3]+…+d[0])

  • according to my understanding the dp[n-1] and dp[n-2] is due to domino

  • and the 2*(dp[n-3]+…+d[0]) is due to tromino

  • can someone explain why the total number of tiling
    for the trominos is 2*(dp[n-3]+…+d[0]);

or if i am wrong please correct me!!

please help!!!