Steps

steps.rs

 #![feature(inclusive_range_syntax)]

/// Steps At
///
/// Returns the number of combinations of steps which can be made
/// where the top step is a given size. This is used as the recursive
/// step.
///
/// # Arguments
///
///  * `top_step` - The size of the top step
///  * `remaining_bricks` - The number of leftover bricks that can be used.
fn steps_at(top_step: usize, remaining_bricks: usize) -> usize {

    if remaining_bricks > ((2 * top_step) + 2) {
        // If we have enough to potentially make two layers of bricks
        ((top_step + 1)...(remaining_bricks / 2))
            .map(|i| { steps_at(i, remaining_bricks - i)})
            .sum::<usize>() + 1
    } else if remaining_bricks > top_step {
        // Just enough for a single layer of bricks
        1
    } else {
        // Not enough leftover bricks to make a layer
        0
    }
}

/// Steps
///
/// Computes the number of possible steps whic can be created with a
/// given number of bricks.
///
/// # Arguments
///
///  * `i` - The number of bricks available
fn steps(i: usize) -> usize {
    (1...i/2)
        .map(|j| { steps_at(j, i - j)})
        .sum()
}

fn main() {

    for i in 1..200 {
        println!("{}: {}", i, steps(i));
    }
}