cp's OEIS Frontend

A358726 Difference between the node-height and the number of leaves in the rooted tree with Matula-Goebel number n.

%I A358726 #5 Dec 01 2022 08:55:56
%S A358726 0,1,2,0,3,1,1,-1,1,2,4,0,2,0,2,-2,2,0,0,1,0,3,2,-1,2,1,0,-1,3,1,5,-3,
%T A358726 3,1,1,-1,1,-1,1,0,3,-1,1,2,1,1,3,-2,-1,1,1,0,-1,-1,3,-2,-1,2,3,0,1,4,
%U A358726 -1,-4,1,2,1,0,1,0,2,-2,1,0,1,-2,2,0,4,-1
%N A358726 Difference between the node-height and the number of leaves in the rooted tree with Matula-Goebel number n.
%C A358726 Node-height is the number of nodes in the longest path from root to leaf.
%C A358726 The Matula-Goebel number of a rooted tree is the product of primes indexed by the Matula-Goebel numbers of the branches of its root, which gives a bijective correspondence between positive integers and unlabeled rooted trees.
%F A358726 a(n) = A358552(n) - A109129(n).
%e A358726 The tree (oo(oo(o))) with Matula-Goebel number 148 has node-height 4 and 5 leaves, so a(148) = -1.
%t A358726 MGTree[n_]:=If[n==1,{},MGTree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A358726 Table[(Depth[MGTree[n]]-1)-Count[MGTree[n],{},{0,Infinity}],{n,1000}]
%Y A358726 Positions of first appearances are A007097 and latter terms of A000079.
%Y A358726 Positions of 0's are A358577.
%Y A358726 Other differences: A358580, A358724, A358729.
%Y A358726 A000081 counts rooted trees, ordered A000108.
%Y A358726 A034781 counts rooted trees by nodes and height, ordered A080936.
%Y A358726 A055277 counts rooted trees by nodes and leaves, ordered A001263.
%Y A358726 MG statistics: A061775, A109082, A109129, A196050, A342507, A358552.
%Y A358726 MG core: A000040, A000720, A001222, A056239, A112798.
%Y A358726 Cf. A185650, A206487, A209638, A358576, A358578, A358587, A358730.
%K A358726 sign
%O A358726 1,3
%A A358726 _Gus Wiseman_, Nov 29 2022