Chessboard rectangles sequence (see Comments), also A037270 interleaved with A163102.

Terms

a(0) =0a(1) =0a(2) =1a(3) =2a(4) =10a(5) =18a(6) =45a(7) =72a(8) =136a(9) =200a(10) =325a(11) =450a(12) =666a(13) =882a(14) =1225a(15) =1568a(16) =2080a(17) =2592a(18) =3321a(19) =4050a(20) =5050a(21) =6050a(22) =7381a(23) =8712a(24) =10440a(25) =12168a(26) =14365a(27) =16562a(28) =19306a(29) =22050