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A184941 Irregular triangle C(n,g) counting the connected 4-regular simple graphs on n vertices with girth at least g. 7
1, 1, 2, 6, 1, 16, 0, 59, 2, 265, 2, 1544, 12, 10778, 31, 88168, 220, 805491, 1606, 8037418, 16828, 86221634, 193900, 985870522, 2452818, 11946487647, 32670330, 1, 152808063181, 456028474, 2, 2056692014474, 6636066099, 8, 28566273166527, 100135577747, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,3

COMMENTS

The first column is for girth at least 3. The row length sequence starts: 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4. The row length is incremented to g-2 when n reaches A037233(g).

LINKS

Table of n, a(n) for n=5..41.

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

EXAMPLE

1;

1;

2;

6, 1;

16, 0;

59, 2;

265, 2;

1544, 12;

10778, 31;

88168, 220;

805491, 1606;

8037418, 16828;

86221634, 193900;

985870522, 2452818;

11946487647, 32670330, 1;

152808063181, 456028474, 2;

2056692014474, 6636066099, 8;

28566273166527, 100135577747, 131;

CROSSREFS

Connected 4-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A006820 (g=3), A033886 (g=4), A058343 (g=5), A058348 (g=6).

Connected 4-regular simple graphs with girth exactly g: A184940 (triangle); chosen g: A184943 (g=3), A184944 (g=4), A184945 (g=5), A184946 (g=6).

Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g: A185131 (k=3), this sequence (k=4), A184951 (k=5), A184961 (k=6), A184971 (k=7), A184981 (k=8).

Sequence in context: A109530 A264789 A111519 * A185340 A280568 A280836

Adjacent sequences:  A184938 A184939 A184940 * A184942 A184943 A184944

KEYWORD

nonn,hard,tabf

AUTHOR

Jason Kimberley, Jan 10 2012

STATUS

approved

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Last modified June 6 17:20 EDT 2020. Contains 334829 sequences. (Running on oeis4.)