[seqfan] Re: More terms for A185074 (editing).

[Richard Mathar]

http://list.seqfan.eu/pipermail/seqfan/2012-March/016529.html

jl> Joerg Arndt feels that A185074 <https://oeis.org/A185074> (Number of 
jl> representations of n in the form sum(i=1..n, c(i)/i ), where each of the 
jl> c(i)'s is in {0,1,...,n}.), submitted recently, needs more terms before 


I added 1274, 9443 and 54094 obtained with the following recursive Java program:

import java.math.* ;
class A185074 {

    int n ;
    A185074(int n)
    {
        this.n = n ;
    }

    static BigInteger factorial(int n)
    {
        BigInteger res = BigInteger.ONE ;
        for(int i=2; i <= n ; i++)
            res = res.multiply(new BigInteger(""+i)) ;
        return res ;
    }

    int compute()
    {
        /* sum_i c(i)/i = n
        * sum_i c(i)n!/i = n*n!
        */
        BigInteger nfa = factorial(n) ;
        return compute(1, nfa.multiply(new BigInteger(""+n)),nfa) ;
    }

    int compute(int lowi, BigInteger target, BigInteger nfa)
    {
        int cnt =0 ;
        BigInteger su = BigInteger.ZERO ;
        for(int c=0 ; c <= n ; c++)
        {
            su = new BigInteger(""+c).multiply(nfa).divide(new BigInteger(""+lowi)) ;
            if ( su.compareTo(target) > 0 )
                break;
            if ( lowi == n)
            {
                if ( su.compareTo(target) == 0 )
                    cnt++;
            }
            else
                cnt += compute(lowi+1, target.subtract(su), nfa) ;
        }
        return cnt ;
    }

    static public void main(String[] args)
    {
        for(int n=1; n < 100 ; n++)
        {
            A185074 oeis  = new A185074(n) ;
            System.out.println(n + " " + oeis.compute()) ;
        }
    }
}