Number of carbon (rooted) trees with n carbon atoms = unordered 4-tuples of ternary trees.

Terms

a(0) =0a(1) =1a(2) =1a(3) =2a(4) =4a(5) =9a(6) =18a(7) =42a(8) =96a(9) =229a(10) =549a(11) =1347a(12) =3326a(13) =8330a(14) =21000a(15) =53407a(16) =136639a(17) =351757a(18) =909962a(19) =2365146a(20) =6172068a(21) =16166991a(22) =42488077a(23) =112004630a(24) =296080425a(25) =784688263a(26) =2084521232a(27) =5549613097a(28) =14804572332a(29) =39568107511