a(n) = Sum_{k=1..floor((n+1)/2)} T(n,2k-1), array T as in A049777.

Terms

a(0) =1a(1) =3a(2) =9a(3) =17a(4) =32a(5) =50a(6) =78a(7) =110a(8) =155a(9) =205a(10) =271a(11) =343a(12) =434a(13) =532a(14) =652a(15) =780a(16) =933a(17) =1095a(18) =1285a(19) =1485a(20) =1716a(21) =1958a(22) =2234a(23) =2522a(24) =2847a(25) =3185a(26) =3563a(27) =3955a(28) =4390a(29) =4840