#include <stdio.h>
#include <gmp.h>
#define CHECK_BIT(var,pos) (((var) & (pos)) ? 1LL : 0LL)
#define n 9
#if n%2==0
  #define NODD 0
#else
  #define NODD 1
#endif

mpz_t bigsum;
mpz_t tmp;
unsigned int k;
long long int prod[n];

inline void updatesum(unsigned int odd)
{
    mpz_set_si(tmp,1);
    for(k=0; k < n; k++)
    {
      if(prod[k] == 0LL) 
      {
	return;
      }
      mpz_mul_si(tmp,tmp,prod[k]);
    }
    if(NODD)
      mpz_mul_si(tmp,tmp, -1);
    if(odd) mpz_sub(bigsum,bigsum,tmp);
    else mpz_add(bigsum,bigsum,tmp);
}

int main()
{
  unsigned long long int i,swp,min;
  unsigned long long int gray = 0;
  unsigned long long int bigN = (1LL<<(3*n));
  mpz_init(bigsum);
  mpz_init(tmp);
  for (k=0; k < n; k++) prod[k] = 0LL;
  for(i=0LL; i < bigN; i++)
  {
    min = i & (-i); // bit changed in graycode
    gray ^= min; // graycode

    if(min&gray) // +1
    {

      swp=min>>1;
      for (k=0; k < n && swp>>(k+1); swp>>=1)
      {
	prod[k] += CHECK_BIT(gray,swp)*CHECK_BIT(gray,swp>>(k+1));
      }

      swp=min<<1;
      for (k=0; k < n && swp<<(k+1) < bigN; k++, swp<<=1)
      {
	prod[k] += CHECK_BIT(gray,swp)*CHECK_BIT(gray,swp<<(k+1));
      }
    }
    else // 0
    {
      swp=min>>1;
      for (k=0; k < n && swp>>(k+1); swp>>=1)
      {
	prod[k] -= CHECK_BIT(gray,swp)*CHECK_BIT(gray,swp>>(k+1));
      }

      swp=min<<1;
      for (k=0; k < n && swp<<(k+1) < bigN; k++, swp<<=1)
      {
	prod[k] -= CHECK_BIT(gray,swp)*CHECK_BIT(gray,swp<<(k+1));
      }
    }
    updatesum(i&1);
  }
  gmp_printf("Triplet Skolem sequences of order %d: %Zd\n", n, bigsum);
}