Upper (2/3)-midsequence of binomial(n,3) and binomial(n,2); see Comments.

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =7a(5) =14a(6) =24a(7) =38a(8) =56a(9) =80a(10) =110a(11) =147a(12) =191a(13) =243a(14) =304a(15) =374a(16) =454a(17) =544a(18) =646a(19) =760a(20) =887a(21) =1027a(22) =1181a(23) =1350a(24) =1534a(25) =1734a(26) =1950a(27) =2184a(28) =2436a(29) =2707