a(1) = 1, a(n+1)= smallest triangular number greater than the n-th partial sum.

Terms

a(0) =1a(1) =3a(2) =6a(3) =15a(4) =28a(5) =55a(6) =120a(7) =231a(8) =465a(9) =946a(10) =1891a(11) =3828a(12) =7626a(13) =15225a(14) =30628a(15) =61075a(16) =122265a(17) =244650a(18) =489555a(19) =979300a(20) =1959210a(21) =3918600a(22) =7838820a(23) =15677200a(24) =31359240a(25) =62714400a(26) =125429041a(27) =250868800a(28) =501732003a(29) =1003497600