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

1,2

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).

Links

Table of n, a(n) for n=1..55.

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

Example

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.

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}]

Crossrefs

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

Sequence in context: A302498 A243497 A214577 * A138039 A289995 A192137

Adjacent sequences: A280991 A280992 A280993 * A280995 A280996 A280997

Keyword

nonn,tabf

Author

Gus Wiseman, Jan 12 2017

Status

approved