a(n) is the maximum value of the quartet index of a bifurcating rooted tree with n leaves.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =3a(5) =9a(6) =19a(7) =38a(8) =64a(9) =106a(10) =162a(11) =243a(12) =343a(13) =479a(14) =645a(15) =860a(16) =1110a(17) =1424a(18) =1790a(19) =2237a(20) =2743a(21) =3349a(22) =4035a(23) =4842a(24) =5734a(25) =6770a(26) =7920a(27) =9239a(28) =10679a(29) =12315