a(n) is the number of triangular partitions whose Young diagram fits inside a square of side n.

Terms

a(0) =1a(1) =2a(2) =5a(3) =12a(4) =25a(5) =48a(6) =83a(7) =136a(8) =211a(9) =314a(10) =449a(11) =626a(12) =849a(13) =1130a(14) =1475a(15) =1892a(16) =2389a(17) =2982a(18) =3677a(19) =4492a(20) =5435a(21) =6518a(22) =7751a(23) =9156a(24) =10741a(25) =12526a(26) =14523a(27) =16750a(28) =19219a(29) =21958