Fractional part of square root of a(n) starts with 4: first term of runs.

Terms

a(0) =2a(1) =6a(2) =12a(3) =20a(4) =30a(5) =41a(6) =55a(7) =71a(8) =89a(9) =109a(10) =130a(11) =154a(12) =180a(13) =208a(14) =238a(15) =269a(16) =303a(17) =339a(18) =377a(19) =417a(20) =458a(21) =502a(22) =548a(23) =596a(24) =646a(25) =697a(26) =751a(27) =807a(28) =865a(29) =925