a(n) is the number of domino towers with n bricks up to horizontal flipping.

Terms

a(0) =1a(1) =2a(2) =6a(3) =15a(4) =44a(5) =126a(6) =374a(7) =1106a(8) =3307a(9) =9877a(10) =29599a(11) =88675a(12) =265932a(13) =797453a(14) =2392089a(15) =7175294a(16) =21525097a(17) =64572513a(18) =193715253a(19) =581137787a(20) =1743406694a(21) =5230197111a(22) =15690571861a(23) =47071649170a(24) =141214890563a(25) =423644479136