a(n) = s(n+3)/3, where s(n) = A024725(n).

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =7a(5) =10a(6) =22a(7) =46a(8) =88a(9) =175a(10) =343a(11) =757a(12) =1540a(13) =3097a(14) =6445a(15) =13810a(16) =28852a(17) =59563a(18) =124618a(19) =271423a(20) =575566a(21) =1206850a(22) =2562904a(23) =5595625a(24) =11984311a(25) =25458607a(26) =54441703a(27) =119591221a(28) =257882038a(29) =552163087