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 A318049 Number of first/rest balanced rooted plane trees with n nodes. 4
 1, 0, 1, 0, 1, 1, 1, 3, 2, 6, 8, 11, 26, 28, 67, 96, 162, 316, 448, 922 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS A rooted plane tree is first/rest balanced if either (1) it is a single node, or (2a) the number of leaves in the first branch is equal to the number of branches minus one, and (2b) every branch is also first/rest balanced. Also the number of composable free pure multifunctions (CPMs) with one atom and n positions. A CPM is either (case 1) the leaf symbol "o", or (case 2) an expression of the form h[g_1, ..., g_k] where h and each of the g_i for i = 1, ..., k > 0 are CPMs, and the number of leaves in h is equal to k. The number of positions in a CPM is the number of brackets [...] plus the number of o's. LINKS EXAMPLE The a(12) = 11 first/rest balanced rooted plane trees:   (o(o(o((oo)oo))))   (o(o((oo)(oo)o)))   (o(o((oo)o(oo))))   (o((oo)(o(oo))o))   (o((oo)o(o(oo))))   (o((oo)(oo)(oo)))   ((oo)(o(o(oo)))o)   ((oo)o(o(o(oo))))   ((o(o(oo)))oooo)   ((oo)(o(oo))(oo))   ((oo)(oo)(o(oo))) The a(12) = 11 composable free pure multifunctions:   o[o[o[o[o][o,o]]]]   o[o[o[o][o[o],o]]]   o[o[o[o][o,o[o]]]]   o[o[o][o[o[o]],o]]   o[o[o][o,o[o[o]]]]   o[o[o][o[o],o[o]]]   o[o][o[o[o[o]]],o]   o[o][o,o[o[o[o]]]]   o[o][o[o[o]],o[o]]   o[o][o[o],o[o[o]]]   o[o[o[o]]][o,o,o,o] MATHEMATICA balplane[n_]:=balplane[n]=If[n===1, {{}}, Join@@Function[c, Select[Tuples[balplane/@c], Length[Cases[#[[1]], {}, {0, Infinity}]]==Length[#]-1&]]/@Join@@Permutations/@IntegerPartitions[n-1]]; Table[Length[balplane[n]], {n, 10}] CROSSREFS Cf. A000081, A000108, A001003, A001006, A007853, A126120, A317713, A318046, A318048. Sequence in context: A131006 A122362 A072635 * A210754 A210738 A210601 Adjacent sequences:  A318046 A318047 A318048 * A318050 A318051 A318052 KEYWORD nonn,more AUTHOR Gus Wiseman, Aug 13 2018 STATUS approved

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Last modified March 20 20:14 EDT 2019. Contains 321352 sequences. (Running on oeis4.)