a(1) = 1; a(n+1) = a(n) + (largest triangular number <= a(n)).

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =12a(5) =22a(6) =43a(7) =79a(8) =157a(9) =310a(10) =610a(11) =1205a(12) =2381a(13) =4727a(14) =9383a(15) =18699a(16) =37227a(17) =74355a(18) =148660a(19) =296900a(20) =593735a(21) =1187240a(22) =2373810a(23) =4746741a(24) =9491481a(25) =18981027a(26) =37956907a(27) =75910735a(28) =151820416a(29) =303627016