Count total number of N digit numbers such that the difference between sum of even and odd digits is 1

<script>

// A memoization based recursive 
// program to count numbers with 
// difference between odd and 
// even digit sums as 1

// A lookup table used for memoization.
let lookup = new Array(50);
for(let i=0;i<50;i++)
{
    lookup[i]=new Array(1000);
    for(let j=0;j<1000;j++)
    {
        lookup[i][j]=new Array(1000);
        for(let k=0;k<1000;k++)
        {
            lookup[i][j][k]=new Array(2);
        }
        
    }
}

// Memoization based recursive 
// function to count numbers
// with even and odd digit sum 
// difference as 1. This function
// considers leading zero as a digit
function countRec(digits,esum,osum,isOdd,n)
{
    // Base Case
    if (digits == n)
        return (esum - osum == 1)?1:0;
  
    // If current subproblem is already computed
    if (lookup[digits][esum][osum][isOdd] != -1)
        return lookup[digits][esum][osum][isOdd];
  
    // Initialize result
    let ans = 0;
  
    // If current digit is odd, then
    // add it to odd sum and recur
    if (isOdd==1)
    for (let i = 0; i <= 9; i++)
        ans += countRec(digits+1, esum, osum+i, 0, n);
    else // Add to even sum and recur
    for (let i = 0; i <= 9; i++)
        ans += countRec(digits+1, esum+i, osum, 1, n);
  
    // Store current result in lookup 
    // table and return the same
    return lookup[digits][esum][osum][isOdd] = ans;
}

// This is mainly a wrapper over countRec. It
// explicitly handles leading digit and calls
// countRec() for remaining digits.
function finalCount(n)
{
    // Initialize number digits considered so far
    let digits = 0;
  
    // Initialize all entries of lookup table
    for(let i = 0; i < 50; i++)
        for(let j = 0; j < 1000; j++)
            for(let k = 0; k < 1000; k++)
                for(let l = 0; l < 2; l++)
                    lookup[i][j][k][l] = -1;
  
  
    // Initialize final answer
    let ans = 0;
  
    // Initialize even and odd sums
    let esum = 0, osum = 0;
  
    // Explicitly handle first digit and 
    // call recursive function countRec 
    // for remaining digits. Note that
    // the first digit is considered 
    // as even digit.
    for (let i = 1; i <= 9; i++)
        ans += countRec(digits+1, esum + i, osum, 1, n);
  
    return ans;
}

// Driver program
let n = 3;
document.write("Count of "+ n + 
            " digit numbers is " + finalCount(n));


// This code is contributed by rag2127

</script>