

A263104


a(3k), a(3k+1), a(3k+2) are the numbers of edges between each vertexpair in a multigraph with 3 vertices and k edges (with at least one edge between each vertexpair) which has the minimum number of distinct cycles, if that arrangement of edges is unique.


3



1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 3, 2, 2, 3, 2, 3, 3, 1, 4, 4, 3, 3, 4, 3, 4, 4, 2, 5, 5, 4, 4, 5, 4, 5, 5, 3, 6, 6, 5, 5, 6, 5, 6, 6, 4, 7, 7, 6, 6, 7, 6, 7, 7, 5, 8, 8, 7, 7, 8, 7, 8, 8, 7, 8, 9, 8, 8, 9, 8, 9, 9, 8, 9, 10
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OFFSET

9,6


COMMENTS

Cycles are counted as in A263103. Each group of three is in ascending order.
The sequence is welldefined for all n checked so far; that is, there are no known k which produce two different multigraphs with the minimal number of cycles.
Viewing the sequence in rows of three (see links) suggests that after a(64) its behavior becomes regular, with each value of a(n) appearing 9 times in 3 contiguous columns of 3 (see conjectured formula).


LINKS

Simon R. Donnelly, Table of n, a(n) for n = 9..280
Simon R. Donnelly, Python program
Eric W. Weisstein, Multigraph


FORMULA

a(n) = floor((n +4*(n%3)1)/9) for n >= 65 (conjectured).


EXAMPLE

For k=6 there are three possible arrangements:
1,1,4: 40 cycles,
1,2,3: 28 cycles(*),
2,2,2: 33 cycles,
so a(18,19,20) = 1,2,3.


PROG

(Python) See links.


CROSSREFS

Sequence in context: A007723 A067437 A242425 * A282518 A230241 A029315
Adjacent sequences: A263101 A263102 A263103 * A263105 A263106 A263107


KEYWORD

nonn,walk,tabf


AUTHOR

Simon R. Donnelly, Oct 09 2015


STATUS

approved



