A210703 -id:A210703 - cp's OEIS frontend

A185033 Number of disconnected 3-regular simple graphs on 2n vertices with girth exactly 3.

0, 0, 0, 0, 1, 2, 8, 29, 138, 774, 5678, 53324, 622716, 8604351, 135344959, 2363662004, 45134533117, 933058713014, 20735549517852, 492653820710746

Offset: 0

Jason Kimberley, Feb 29 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: this sequence (k=3), A185043 (k=4), A185053 (k=5), A185063 (k=6).

Disconnected 3-regular simple graphs with girth exactly g: this sequence (g=3), A185034 (g=4), A185035 (g=5), A185036 (g=6), A185037 (g=7).

a(n) = A165653(n) - A185234(n).

A185043 Number of disconnected 4-regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 8, 25, 88, 377, 2026, 13349, 104593, 930571, 9124627, 96699740, 1095467916, 13175254799, 167460501260, 2241576473025, 31510509517563, 464047467911837, 7143984462730072, 114749034352969037, 1919656978492976231

Offset: 0

Jason Kimberley, Feb 29 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

4-regular simple graphs with girth exactly 3: A184943 (connected), this sequence (disconnected), A185143 (not necessarily connected).
Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: A185033 (k=3), this sequence (k=4), A185053 (k=5), A185063 (k=6).
Disconnected 4-regular simple graphs with girth exactly g: this sequence (g=3), A185044 (g=4).

a(n) = A033483(n) - A185244(n).

Terms a(27)-a(31), due to the extension of A006820 by Andrew Howroyd, from Jason Kimberley, Mar 16 2020

A185643 Triangular array E(n,k) counting, not necessarily connected, k-regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 4, 5, 3, 1, 1, 0, 0, 2, 0, 16, 0, 4, 0, 1, 0, 0, 2, 15, 58, 59, 21, 5, 1, 1, 0, 0, 3, 0, 264, 0, 266, 0, 6, 0, 1, 0, 0, 4, 71, 1535, 7848, 7848, 1547, 94, 9, 1, 1, 0, 0, 5, 0, 10755, 0, 367860, 0, 10786, 0, 10, 0, 1

Offset: 1

Jason Kimberley, Feb 07 2013

			01: 0;
02: 0, 0;
03: 0, 0, 1;
04: 0, 0, 0, 1;
05: 0, 0, 0, 0, 1;
06: 0, 0, 1, 1, 1, 1;
07: 0, 0, 1, 0, 2, 0, 1;
08: 0, 0, 1, 4, 5, 3, 1, 1;
09: 0, 0, 2, 0, 16, 0, 4, 0, 1;
10: 0, 0, 2, 15, 58, 59, 21, 5, 1, 1;
11: 0, 0, 3, 0, 264, 0, 266, 0, 6, 0, 1;
12: 0, 0, 4, 71, 1535, 7848, 7848, 1547, 94, 9, 1, 1;
13: 0, 0, 5, 0, 10755, 0, 367860, 0, 10786, 0, 10, 0, 1;
14: 0, 0, 6, 428, 87973, 3459379, 21609300, 21609300, 3459386, 88193, 540, 13, 1, 1;
15: 0, 0, 9, 0, 803973, 0, 1470293675, 0, 1470293676, 0, 805579, 0, 17, 0, 1;
16: 0, 0, 10, 3406, 8020967, 2585136353, 113314233804, 733351105934, 733351105934, 113314233813, 2585136741, 8037796, 4207, 21, 1, 1;

Jason Kimberley, Table of i, a(i)=E(n,k) for i = 1..136 (n = 1..16)
Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g

The sum of the n-th row of this sequence is A198313(n).

Not necessarily connected k-regular simple graphs girth exactly 3: A198313 (any k), this sequence (triangle); fixed k: A026796 (k=2), A185133 (k=3), A185143 (k=4), A185153 (k=5), A185163 (k=6).

E(n,k) = A186733(n,k) + A210703(n,k), noting that A210703 is a tabf.

E(n,k) = A051031(n,k) - A185304(n,k), noting that A185304 is a tabf.

A185053 Number of disconnected 5-regular simple graphs on 2n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 3, 66, 8029, 3484759, 2595985769, 2815099031409

Offset: 0

Jason Kimberley, Mar 10 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: A185033 (k=3), A185043 (k=4), this sequence (k=5), A185063 (k=6).

a(n) = A165655(n) - A185254(n).

A210713 Number of disconnected regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 5, 4, 16, 13, 64, 98, 597, 2064, 22472, 112814, 4799607, 31138903, 4207941575, 115979716284, 13482672620149

Offset: 0

Jason Kimberley, Apr 02 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

This sequence is the row sum sequence of the triangle A210703.

Disconnected k-regular simple graphs with girth exactly 3: this sequence (any k), A210703 (triangle); for fixed k: A185033 (k=3), A185043 (k=4), A185053 (k=5), A185063 (k=6).

a(n) = A068932(n) - A185214(n).

A185063 Number of disconnected 6-regular simple graphs on n vertices with girth exactly 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 25, 297, 8199, 377004, 22014143, 1493574756, 114880777582, 9919463450854

Offset: 0

Jason Kimberley, Mar 10 2012

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

Disconnected k-regular simple graphs with girth exactly 3: A210713 (any k), A210703 (triangle); for fixed k: A185033 (k=3), A185043 (k=4), A185053 (k=5), this sequence (k=6).

a(n) = A165656(n) - A185264(n).

cp's OEIS Frontend

A185033 Number of disconnected 3-regular simple graphs on 2n vertices with girth exactly 3.

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A185043 Number of disconnected 4-regular simple graphs on n vertices with girth exactly 3.

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A185643 Triangular array E(n,k) counting, not necessarily connected, k-regular simple graphs on n vertices with girth exactly 3.

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A185053 Number of disconnected 5-regular simple graphs on 2n vertices with girth exactly 3.

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A210713 Number of disconnected regular simple graphs on n vertices with girth exactly 3.

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A185063 Number of disconnected 6-regular simple graphs on n vertices with girth exactly 3.

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