(d(n)-r(n))/2, where d = A008778 and r is the periodic sequence with fundamental period (1,1,0,1).

Terms

a(0) =2a(1) =6a(2) =13a(3) =22a(4) =35a(5) =52a(6) =74a(7) =100a(8) =132a(9) =170a(10) =215a(11) =266a(12) =325a(13) =392a(14) =468a(15) =552a(16) =646a(17) =750a(18) =865a(19) =990a(20) =1127a(21) =1276a(22) =1438a(23) =1612a(24) =1800a(25) =2002a(26) =2219a(27) =2450a(28) =2697a(29) =2960