This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A320271 #4 Oct 09 2018 15:12:54 %S A320271 1,1,2,3,6,9,17,26,46,72,124,196,329,525,871,1396,2293,3689,6028,9717, %T A320271 15817,25534,41475,67009,108680,175689,284698,460387,745610,1205997, %U A320271 1952478,3158475,5112349,8270824,13385466,21656290,35045445,56701735,91753208 %N A320271 Number of unlabeled semi-binary rooted trees with n nodes in which the non-leaf branches directly under any given node are all equal. %C A320271 An unlabeled rooted tree is semi-binary if all out-degrees are <= 2. The number of semi-binary trees with n nodes is equal to the number of binary trees with n+1 leaves; see A001190. %F A320271 a(1) = 1, %F A320271 a(2) = 1, %F A320271 a(3) = 2, %F A320271 a(n even) = a(n-1) + a(n-2), %F A320271 a(n odd) = a(n-1) + a(n-2) + a((n-1)/2). %e A320271 The a(1) = 1 through a(7) = 17 semi-binary rooted trees: %e A320271 o (o) (oo) ((oo)) (o(oo)) ((o(oo))) ((oo)(oo)) %e A320271 ((o)) (o(o)) (((oo))) (o((oo))) (o(o(oo))) %e A320271 (((o))) ((o)(o)) (o(o(o))) (((o(oo)))) %e A320271 ((o(o))) ((((oo)))) ((o((oo)))) %e A320271 (o((o))) (((o)(o))) ((o(o(o)))) %e A320271 ((((o)))) (((o(o)))) (o(((oo)))) %e A320271 ((o((o)))) (o((o)(o))) %e A320271 (o(((o)))) (o((o(o)))) %e A320271 (((((o))))) (o(o((o)))) %e A320271 (((((oo))))) %e A320271 ((((o)(o)))) %e A320271 ((((o(o))))) %e A320271 (((o))((o))) %e A320271 (((o((o))))) %e A320271 ((o(((o))))) %e A320271 (o((((o))))) %e A320271 ((((((o)))))) %t A320271 crb[n_]:=Switch[n,1,1,2,1,3,2,_?EvenQ,crb[n-1]+crb[n-2],_?OddQ,crb[n-1]+crb[n-2]+crb[(n-1)/2]] %t A320271 Array[crb,20] %Y A320271 Cf. A001190, A003238, A111299, A126656, A292050, A298204, A301345, A317712, A320222, A320230, A320270. %K A320271 nonn %O A320271 1,3 %A A320271 _Gus Wiseman_, Oct 08 2018