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Terraced Shell Count

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Picture a shell display that keeps growing in little terraces. At the very beginning there is only one shell. Then each new terrace makes the pattern larger by building on the whole shape that came before it.

Your job is to find out how many shells appear after a certain number of tiers. This is a recursive growth puzzle, which means each new answer depends on the earlier answer. The pattern does not restart from zero every time. It grows from the last stage and adds more structure around it.

For example, when tiers = 0, the answer is 1. When tiers = 1, the display grows to 6. By the time tiers = 3, it reaches 36. So the numbers grow quickly, and the important part is seeing how one stage leads to the next.

The base case matters here because it tells you where the whole pattern begins. After that, each new tier uses the earlier total to make a larger one. So the real challenge is finding the rule that connects one tier count to the next.

Example Input & Output

Example 1
Input
tiers = 3
Output
36
Explanation

Three additional terraces mean another guiding shell plus twin reflections of everything from tier two.

Example 2
Input
tiers = 0
Output
1
Explanation

Only the original shell is shown.

Example 3
Input
tiers = 1
Output
6
Explanation

The new terrace adds one guiding shell and mirrors the earlier display twice.

Algorithm Flow

Recommendation Algorithm Flow for Terraced Shell Count
Recommendation Algorithm Flow for Terraced Shell Count

Best Answers

java
import java.util.*;
class Solution {
    public int calculate_shell_count(Object shell) {
        if (shell instanceof Integer) return (int) shell;
        if (shell instanceof List) {
            int total = 0;
            for (Object item : (List) shell) total += calculate_shell_count(item);
            return total;
        }
        return 0;
    }
}