A097857 a(0) = 1, a(1) = 1, a(n) = floor((a(n-1)+a(n-2))/2) + 3 if a(n-2) is even, a(n) = floor((a(n-1)-a(n-2))/2) + 3 if a(n-2) is odd.

1, 1, 3, 4, 3, 6, 4, 8, 9, 11, 4, 1, 4, 5, 7, 4, 1, 5, 5, 3, 2, 2, 5, 6, 3, 7, 5, 2, 1, 4, 4, 7, 8, 3, 8, 5, 9, 5, 1, 1, 3, 4, 3, 6, 4, 8, 9, 11, 4, 1, 4, 5, 7, 4, 1, 5, 5, 3, 2, 2, 5, 6, 3, 7, 5, 2, 1, 4, 4, 7, 8, 3, 8, 5, 9, 5, 1, 1, 3, 4, 3, 6, 4, 8, 9, 11, 4, 1, 4, 5, 7, 4, 1, 5, 5, 3, 2, 2, 5, 6, 3, 7, 5, 2, 1, 4, 4, 7, 8, 3, 8, 5, 9, 5