a(n) = s(n+3)/3, where s is A024947.

Terms

a(0) =1a(1) =1a(2) =4a(3) =7a(4) =10a(5) =22a(6) =46a(7) =88a(8) =175a(9) =343a(10) =820a(11) =1693a(12) =3448a(13) =7399a(14) =16807a(15) =36322a(16) =76609a(17) =166144a(18) =378730a(19) =831706a(20) =1796773a(21) =3959785a(22) =9004330a(23) =20002942a(24) =43959124a(25) =97356997a(26) =223477834a(27) =500128180a(28) =1109072953a(29) =2483239909