A120152 a(1)=6; a(n)=floor((19+sum(a(1) to a(n-1)))/3).

6, 8, 11, 14, 19, 25, 34, 45, 60, 80, 107, 142, 190, 253, 337, 450, 600, 800, 1066, 1422, 1896, 2528, 3370, 4494, 5992, 7989, 10652, 14203, 18937, 25249, 33666, 44888, 59850, 79800, 106400, 141867, 189156, 252208, 336277, 448370