A085761 Number of triangular numbers between n and 2n (inclusive).

1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7