A280994 Triangle read by rows giving Matula-Goebel numbers of planted achiral trees with n nodes.

1, 2, 3, 4, 5, 7, 8, 9, 11, 16, 17, 19, 23, 31, 32, 53, 59, 67, 25, 27, 49, 64, 83, 127, 131, 241, 277, 331, 97, 103, 128, 227, 311, 431, 709, 739, 1523, 1787, 2221, 81, 121, 256, 289, 361, 509, 563, 719, 1433, 2063, 3001, 5381, 5623, 12763, 15299, 19577

Offset: 1

Author

Gus Wiseman, Jan 12 2017

Keywords

• nonn
• tabf

Comments

An achiral tree is either (case 1) a single node or (case 2) a finite constant sequence (t,t,..,t) of achiral trees. Only in case 2 is an achiral tree considered to be a generalized Bethe tree (according to A214577).

Examples

			Triangle begins:
1,
2,
3, 4,
5, 7, 8,
9, 11, 16, 17, 19,
23, 31, 32, 53, 59, 67,
25, 27, 49, 64, 83, 127, 131, 241, 277, 331.
		

Links

• E. Deutsch, Rooted tree statistics from Matula numbers, arXiv:1111.4288 [math.CO], 2011.

Crossrefs

Cf. A003238 (row lengths), A214577, A061773, A061775, A004111, A007097, A196545, A275870.

Programs

Mathematica

nn=7;MGNumber[[]]:=1;MGNumber[x:[__]]:=If[Length[x]===1,Prime[MGNumber[x[[1]]]],Times@@Prime/@MGNumber/@x];
cits[n_]:=If[n===1,{1},Join@@Table[ConstantArray[#,(n-1)/d]&/@cits[d],{d,Divisors[n-1]}]];
Table[Sort[MGNumber/@(cits[n]/.(1->{}))],{n,nn}]