tozeck(n) = {
	for (i=0, oo,
		if (n<=fibonacci(2+i),
			my (v=0, f);
			forstep (j=i, 0, -1,
				if (n>=f=fibonacci(2+j),
					n-=f;
					v+=2^j;
				);
				if (n==0,
					return (v);
				);
			);
		);
	);
}

fromzeck(n) = {
	my (v=0, j);
	while (n,
		n-=2^j=valuation(n,2);
		v+=fibonacci(2+j);
	);
	return (v);
}

todualzeck(n) = {
    my (s=0, v=0);
    for (i=0, oo,
        if (s>=n,
            forstep (j=i-1, 0, -1,
                if (s-fibonacci(2+j)>=n,
                    s-=fibonacci(2+j);
                    v-=2^j;
                );
            );
            return (v);
        );
        s+=fibonacci(2+i);
        v+=2^i;
    );
}

row(n) = {
	my (z = todualzeck(n), r = vector(hammingweight(z)), b);
	for (k=1, #r,
		z -= b = 2^valuation(z, 2);
		r[k] = fromzeck(b);
	);
	r
}

{
	m = 0;
	for (n = 1, fibonacci(16)-2,
		r = row(n);
		apply (v -> print (m++ " " v), r);
	);
}

quit