# UVa 900

## 900 - Brick Wall Patterns[edit]

## Summary[edit]

Given wall bricks of size units, what is the number of all possible brick patterns for a wall of height units and a length of units?

## Explanation[edit]

Let be the number of ways to assembly a wall of length .

There are two ways of assembling a wall of length , *and a height of 2 units*. We either place a vertical bar at its beginning and assemble a wall of length or we place two horizontal bars on top of one another and assemble then a wall of length . That is,

- .

The base cases are already given in the example, which leads us to:

Which is the fibonacci series, with a slightly different base! (This proof was originally written by Schultz, on 21:20, 26 May 2007 (EDT))

You can solve the series blazingly fast in using a bottom-up dynamic programming solution.

## Gotchas[edit]

Use a 64-bit field to hold the results; .

## Input[edit]

1 2 3 4 5 6 7 50 0

## Output[edit]

1 2 3 5 8 13 21 20365011074