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A068934 Triangular array C(n, r) = number of connected r-regular graphs with n nodes, 0 <= r < n. 31
1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 2, 1, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 5, 6, 3, 1, 1, 0, 0, 1, 0, 16, 0, 4, 0, 1, 0, 0, 1, 19, 59, 60, 21, 5, 1, 1, 0, 0, 1, 0, 265, 0, 266, 0, 6, 0, 1, 0, 0, 1, 85, 1544, 7848, 7849, 1547, 94, 9, 1, 1, 0, 0, 1, 0, 10778, 0, 367860, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,19

COMMENTS

A graph is called r-regular if every node has exactly r edges. The numbers in this table were copied from the column sequences.

LINKS

Jason Kimberley, Rows 1..16 of A068934 triangle, flattened

Jason Kimberley, Connected regular graphs (with girth at least 3)

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

Zhipeng Xu, Xiaolong Huang, Fabian Jimenez, Yuefan Deng, A new record of enumeration of regular graphs by parallel processing, arXiv:1907.12455 [cs.DM], 2019.

FORMULA

C(n, r) = A051031(n, r) - A068933(n, r).

EXAMPLE

01: 1;

02: 0, 1;

03: 0, 0, 1;

04: 0, 0, 1, 1;

05: 0, 0, 1, 0, 1;

06: 0, 0, 1, 2, 1, 1;

07: 0, 0, 1, 0, 2, 0, 1;

08: 0, 0, 1, 5, 6, 3, 1, 1;

09: 0, 0, 1, 0, 16, 0, 4, 0, 1;

10: 0, 0, 1, 19, 59, 60, 21, 5, 1, 1;

11: 0, 0, 1, 0, 265, 0, 266, 0, 6, 0, 1;

12: 0, 0, 1, 85, 1544, 7848, 7849, 1547, 94, 9, 1, 1;

13: 0, 0, 1, 0, 10778, 0, 367860, 0, 10786, 0, 10, 0, 1;

14: 0, 0, 1, 509, 88168, 3459383, 21609300, 21609301, 3459386, 88193, 540, 13, 1, 1;

15: 0, 0, 1, 0, 805491, 0, 1470293675, 0, 1470293676, 0, 805579, 0, 17, 0, 1;

16: 0, 0, 1, 4060, 8037418, 2585136675, 113314233808, 733351105934, 733351105935, 113314233813, 2585136741, 8037796, 4207, 21, 1, 1;

CROSSREFS

Connected regular simple graphs: A005177 (any degree -- sum of rows), this sequence (triangular array), specified degree r (columns): A002851 (r=3), A006820 (r=4), A006821 (r=5), A006822 (r=6), A014377 (r=7), A014378 (r=8), A014381 (r=9), A014382 (r=10), A014384 (r=11).

Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth *at least* g: this sequence (g=3), A186714 (g=4), A186715 (g=5), A186716 (g=6), A186717 (g=7), A186718 (g=8), A186719 (g=9).

Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth *exactly* g: A186733 (g=3), A186734 (g=4).

Sequence in context: A081227 A301469 A004610 * A035200 A198066 A141664

Adjacent sequences:  A068931 A068932 A068933 * A068935 A068936 A068937

KEYWORD

nonn,tabl,hard,changed

AUTHOR

David Wasserman, Mar 08 2002

EXTENSIONS

Edited by Jason Kimberley, Sep 23 2009, Nov 2011, Jan 2012, and Mar 2012

STATUS

approved

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Last modified October 23 14:11 EDT 2019. Contains 328345 sequences. (Running on oeis4.)