Let b(0)=1/2, b(n) = b(n-1) + Prime[n]/2; a(n)=b(2*n).

Terms

a(0) =3a(1) =9a(2) =21a(3) =39a(4) =65a(5) =99a(6) =141a(7) =191a(8) =251a(9) =320a(10) =396a(11) =482a(12) =581a(13) =686a(14) =797a(15) =926a(16) =1064a(17) =1214a(18) =1374a(19) =1544a(20) =1724a(21) =1916a(22) =2114a(23) =2331a(24) =2559a(25) =2795a(26) =3041a(27) =3301a(28) =3571a(29) =3850