A360862 - OEIS

A360862

Triangle read by rows: T(n,k) is the number of unlabeled connected multigraphs with n edges on k nodes and degree >= 3 at each node, loops allowed, n >= 2, 1 <= k <= floor(2*n/3).

1, 1, 2, 1, 4, 1, 7, 5, 1, 10, 20, 5, 1, 14, 48, 36, 1, 18, 99, 153, 30, 1, 23, 181, 481, 277, 17, 1, 28, 303, 1239, 1451, 323, 1, 34, 479, 2811, 5572, 2946, 193, 1, 40, 726, 5805, 17607, 17343, 3806, 71, 1, 47, 1055, 11148, 48401, 77708, 36872, 3188, 1, 54, 1492, 20219, 120018, 288476, 243007, 54386, 1496

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,3

COMMENTS

Terms may be computed using the tools geng, vcolg and multig in nauty with some additional processing to check the degrees of nodes.

LINKS

Table of n, a(n) for n=2..66.

Brendan McKay and Adolfo Piperno, nauty and Traces

EXAMPLE

Triangle begins:

1, 2;

1, 4;

1, 7, 5;

1, 10, 20, 5;

1, 14, 48, 36;

1, 18, 99, 153, 30;

1, 23, 181, 481, 277, 17;

1, 28, 303, 1239, 1451, 323;

1, 34, 479, 2811, 5572, 2946, 193;

1, 40, 726, 5805, 17607, 17343, 3806, 71;

1, 47, 1055, 11148, 48401, 77708, 36872, 3188;

1, 54, 1492, 20219, 120018, 288476, 243007, 54386, 1496;

...

CROSSREFS

Column 2 is A014616.

Row sums are A360863.

Diagonal sums are A360864.

Cf. A322115, A327615, A360866 (loopless).

Sequence in context: A115124 A115122 A097360 * A325348 A307683 A248058

Adjacent sequences: A360859 A360860 A360861 * A360863 A360864 A360865

KEYWORD

nonn,tabf

AUTHOR

Andrew Howroyd, Feb 24 2023

STATUS

approved