Count Quoridor wall positions

QuoridorCounter.java

import java.math.BigInteger;
import java.util.*;

public class QuoridorCounter {
	public static void main(String[] args) {
		List<String> rows = new ArrayList<String>();
		char[] chs = new char[8];
		for (int i = 0; i < 6561 /* 3^8 */; i++) {
			int r = i;
			for (int j = 0; j < 8; j++) {
				chs[j] = "HV ".charAt(r % 3);
				r /= 3;
			}

			String row = new String(chs);
			if (row.indexOf("HH") == -1) rows.add(row);
		}

		// Initialise: first row
		BigInteger[][] counts = new BigInteger[rows.size()][21];
		for (int i = 0; i < counts.length; i++) {
			for (int j = 0; j < counts[i].length; j++) {
				counts[i][j] = BigInteger.ZERO;
			}
			int k = 0;
			for (char ch : rows.get(i).toCharArray()) if (ch != ' ') k++;
			counts[i][k] = BigInteger.ONE;
		}

		// Subsequent rows.
		for (int step = 0; step < 7; step++) {
			BigInteger[][] nc = new BigInteger[rows.size()][21];
			for (int i = 0; i < nc.length; i++) {
				for (int j = 0; j < nc[i].length; j++) {
					nc[i][j] = BigInteger.ZERO;
				}
			}

			for (int row1 = 0; row1 < rows.size(); row1++) {
				for (int row2 = 0; row2 < rows.size(); row2++) {
					boolean clash = false;
					for (int i = 0; i < 8; i++) {
						if (rows.get(row1).charAt(i) == 'V' && rows.get(row2).charAt(i) == 'V') clash = true;
					}

					if (clash) continue;

					// row1 can be followed by row2.
					int delta = 0;
					for (char ch : rows.get(row2).toCharArray()) if (ch != ' ') delta++;

					for (int wallCount = 0; wallCount + delta < 21; wallCount++) {
						nc[row2][wallCount + delta] = nc[row2][wallCount + delta].add(counts[row1][wallCount]);
					}
				}
			}

			counts = nc;
		}

		// Final count
		BigInteger total = BigInteger.ZERO;
		for (BigInteger[] byRow : counts) {
			for (BigInteger val : byRow) total = total.add(val);
		}

		System.out.println(total);
	}
}