A120182 a(1)=5; a(n)=floor((34+sum(a(1) to a(n-1)))/6).

5, 6, 7, 8, 10, 11, 13, 15, 18, 21, 24, 28, 33, 38, 45, 52, 61, 71, 83, 97, 113, 132, 154, 179, 209, 244, 285, 332, 388, 452, 528, 616, 718, 838, 978, 1141, 1331, 1553, 1811, 2113