a(n) = Sum_{i=0..n} T(i,n-i) where T is A049627.

Terms

a(0) =1a(1) =4a(2) =8a(3) =14a(4) =22a(5) =34a(6) =48a(7) =68a(8) =92a(9) =122a(10) =156a(11) =200a(12) =248a(13) =308a(14) =374a(15) =448a(16) =530a(17) =628a(18) =732a(19) =854a(20) =984a(21) =1126a(22) =1278a(23) =1452a(24) =1634a(25) =1836a(26) =2050a(27) =2282a(28) =2526a(29) =2798