My solution for https://www.research.ibm.com/haifa/ponderthis/challenges/February2017.html

201702.c

#include <stdio.h>

#ifndef NBITS
#define NBITS 42
#endif

static unsigned long long states[NBITS + 1][7][2 * NBITS] ;
/*                                  step    s     r     */

static inline int next_s(int s, int b) {
    return (6+s*(5+s*s*s*(2+s*(3+s))) + b*(5+s*(5+s*(6+s*s*(3+s*6))))) % 7 ;
}

int main(int ac, const char *av[]) {
    states[0][2][NBITS] = 1 ;

    for (int i = 0; i < NBITS; i ++)
        for (int s = 0; s < 7; s ++)
            for (int r = 1 - NBITS; r < NBITS; r ++) {
                for (int b = 0; b <= 1; b ++) {
                    int r1 = r ;
                    int s1 = next_s(s, b) ;
                    if (b == s) r1 = r + 2 * b - 1 ;
                    states[i + 1][s1][NBITS + r1] += states[i][s][NBITS + r] ;
                }
            }

    unsigned long long cnt = 0 ;
    for (int s = 0; s < 7; s ++)
        for (int r = 1 - NBITS; r < NBITS; r ++)
            if (r) cnt += states[NBITS][s][NBITS + r] ;

    printf("%llu\n", cnt) ;
    return 0 ;
}