a(n) is the number of symmetric domino towers with n bricks.

Terms

a(0) =1a(1) =1a(2) =3a(3) =3a(4) =7a(5) =9a(6) =19a(7) =25a(8) =53a(9) =71a(10) =149a(11) =203a(12) =423a(13) =583a(14) =1209a(15) =1681a(16) =3473a(17) =4863a(18) =10017a(19) =14107a(20) =28987a(21) =41019a(22) =84113a(23) =119513a(24) =244645a(25) =348829a(26) =712987a(27) =1019731a(28) =2081547a(29) =2985097