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A184961 Irregular triangle C(n,g) read by rows, counting the connected 6-regular simple graphs on n vertices with girth at least g. 7
1, 1, 4, 21, 266, 7849, 1, 367860, 0, 21609300, 1, 1470293675, 1, 113314233808, 9, 9799685588936, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,3

COMMENTS

The first column is for girth at least 3. The row length sequence starts: 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3. The row length is incremented to g-2 when n reaches A054760(6,g).

LINKS

Table of n, a(n) for n=7..23.

Andries E. Brouwer, Cages

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

EXAMPLE

Triangle begins:

1;

1;

4;

21;

266;

7849, 1;

367860, 0;

21609300, 1;

1470293675, 1;

113314233808, 9;

9799685588936, 6;

CROSSREFS

Connected 6-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A006822 (g=3), A058276 (g=4).

Connected 6-regular simple graphs with girth exactly g: A184960 (triangle); chosen g: A184963 (g=3), A184964 (g=4).

Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g: A185131 (k=3), A184941 (k=4), A184951 (k=5), this sequence (k=6), A184971 (k=7), A184981 (k=8).

Sequence in context: A184960 A184963 A185163 * A006822 A165627 A324954

Adjacent sequences:  A184958 A184959 A184960 * A184962 A184963 A184964

KEYWORD

nonn,hard,more,tabf

AUTHOR

Jason Kimberley, Jan 10 2012

STATUS

approved

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Last modified November 13 23:48 EST 2019. Contains 329106 sequences. (Running on oeis4.)