(1/3)*s(n+3), where s = A025256.

Terms

a(0) =1a(1) =2a(2) =6a(3) =14a(4) =35a(5) =97a(6) =264a(7) =727a(8) =2059a(9) =5876a(10) =16893a(11) =49085a(12) =143639a(13) =422764a(14) =1251642a(15) =3724276a(16) =11129680a(17) =33393998a(18) =100560903a(19) =303812039a(20) =920617337a(21) =2797335154a(22) =8521230447a(23) =26017690537a(24) =79610304979a(25) =244082395820a(26) =749739211746