a(n) = (n^5 - n)/10, which is always an integer.

Terms

a(0) =0a(1) =3a(2) =24a(3) =102a(4) =312a(5) =777a(6) =1680a(7) =3276a(8) =5904a(9) =9999a(10) =16104a(11) =24882a(12) =37128a(13) =53781a(14) =75936a(15) =104856a(16) =141984a(17) =188955a(18) =247608a(19) =319998a(20) =408408a(21) =515361a(22) =643632a(23) =796260a(24) =976560a(25) =1188135a(26) =1434888a(27) =1721034a(28) =2051112a(29) =2429997