a(n) = s(n+3)/3, where s is A024961.

Terms

a(0) =2a(1) =4a(2) =11a(3) =28a(4) =68a(5) =169a(6) =470a(7) =1276a(8) =3395a(9) =9016a(10) =26240a(11) =74017a(12) =204590a(13) =568120a(14) =1659350a(15) =4770820a(16) =13538480a(17) =38435515a(18) =113673998a(19) =331360936a(20) =955040204a(21) =2757123412a(22) =8185543376a(23) =24071728150a(24) =70215321944a(25) =204746123776a(26) =612178795262