Number of rooted trees with a forbidden limb of length 3.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =7a(5) =15a(6) =35a(7) =81a(8) =195a(9) =473a(10) =1171a(11) =2924a(12) =7396a(13) =18848a(14) =48446a(15) =125311a(16) =326145a(17) =853188a(18) =2242616a(19) =5919197a(20) =15683008a(21) =41694334a(22) =111195166a(23) =297393668a(24) =797475499a(25) =2143631474a(26) =5775002574a(27) =15590201095a(28) =42168292074a(29) =114260967888