Number of rooted trees with a forbidden limb of length 4.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =18a(6) =43a(7) =102a(8) =251a(9) =625a(10) =1584a(11) =4055a(12) =10509a(13) =27451a(14) =72307a(15) =191697a(16) =511335a(17) =1370995a(18) =3693452a(19) =9991671a(20) =27133149a(21) =73934800a(22) =202096673a(23) =553999573a(24) =1522651908a(25) =4195087022a(26) =11583820212a(27) =32052475655a(28) =88860186023