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A185305 Triangular array E(n,k) counting not necessarily connected k-regular simple graphs on n vertices with girth at least 5. 5
1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 0, 2, 0, 1, 1, 3, 2, 1, 0, 3, 0, 1, 1, 4, 9, 1, 0, 5, 0, 1, 1, 6, 49, 1, 0, 7, 0, 1, 1, 9, 455, 1, 0, 10, 0, 1, 1, 1, 13, 5784, 2, 1, 0, 15, 0, 8, 1, 1, 18, 90940, 131, 1, 0, 21, 0, 3917, 1, 1, 26, 1620491, 123859 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,25

COMMENTS

Row sums give A185315.

LINKS

Jason Kimberley, Table of n, a(i)=E(n,k) for i = 1..108 (n = 1..28)

Jason Kimberley, Not necessarily connected k-regular graphs with girth at least 5

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

FORMULA

E(n,k) = A186715(n,k) + A185205(n,k).

EXAMPLE

01: 1;

02: 1, 1;

03: 1, 0;

04: 1, 1;

05: 1, 0, 1;

06: 1, 1, 1;

07: 1, 0, 1;

08: 1, 1, 1;

09: 1, 0, 1;

10: 1, 1, 2, 1;

11: 1, 0, 2, 0;

12: 1, 1, 3, 2;

13: 1, 0, 3, 0;

14: 1, 1, 4, 9;

15: 1, 0, 5, 0;

16: 1, 1, 6, 49;

17: 1, 0, 7, 0;

18: 1, 1, 9, 455;

19: 1, 0, 10, 0, 1;

20: 1, 1, 13, 5784, 2;

21: 1, 0, 15, 0, 8;

22: 1, 1, 18, 90940, 131;

23: 1, 0, 21, 0, 3917;

24: 1, 1, 26, 1620491, 123859;

25: 1, 0, 30, 0, 4131991;

26: 1, 1, 36, 31478649, 132160608;

27: 1, 0, 42, 0, 4018022149;

28: 1, 1, 50, 656784488, 118369811960;

CROSSREFS

Not necessarily connected k-regular simple graphs with girth at least 5: A185315 (any k), this sequence (triangle); specified degree k: A185325 (k=2), A185335 (k=3).

Sequence in context: A253559 A136167 A140748 * A259875 A070821 A165890

Adjacent sequences:  A185302 A185303 A185304 * A185306 A185307 A185308

KEYWORD

nonn,hard,tabf

AUTHOR

Jason Kimberley, Feb 21 2013

STATUS

approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)