A044928 a(n)=so-se, where so(se)=sum of odd(even) base 6 run lengths of n.

1, 1, 1, 1, 1, 2, -2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, -2, -1, 3, 3, 3, 3, 3, -1, 3, -1, -1, -1, -1, 3, 3, -1, 3, 3, 3, 3, 3, 3, -1, 3, 3, 3, 3, 3, 3, -1, 3, 3, 3, 3, 3, 3, -1, -1, 3, 3, 3, 3, 3, 3, -1, 3, 3, 3