A298304 Number of rooted trees on n nodes with strictly thinning limbs.

1, 1, 1, 2, 3, 4, 7, 12, 19, 31, 51, 85, 144, 245, 417, 712, 1221, 2091, 3600, 6216, 10763, 18691, 32546, 56782, 99271, 173849, 304877, 535412, 941385, 1657069, 2919930, 5150546, 9093894, 16071634, 28428838, 50331137, 89181251, 158145233, 280650225, 498410197

Offset: 1

Author

Gus Wiseman, Jan 16 2018

Keywords

• nonn

Comments

An unlabeled rooted tree has strictly thinning limbs if its outdegrees are strictly decreasing from root to leaves.

Examples

			The a(7) = 7 trees: (oo(o(o))), (o(o)(oo)), (ooo(oo)), ((o)(o)(o)), (oo(o)(o)), (oooo(o)), (oooooo).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A000081, A001678, A004111, A032305, A124343, A290689, A295461, A298118, A298303, A298305.

Programs

Mathematica

stinctQ[t_]:=And@@Cases[t,b_List:>Length[b]>Max@@Length/@b,{0,Infinity}];
strut[n_]:=strut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1],stinctQ]];
Table[Length[strut[n]],{n,20}]

Extensions

a(26)-a(40) from Alois P. Heinz, Jan 17 2018