A185207 -id:A185207 - cp's OEIS frontend

A185227 Number of disconnected 2-regular simple graphs on n vertices with girth at least 7.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 14, 17, 19, 23, 26, 31, 35, 41, 47, 55, 62, 72, 82, 95, 107, 124, 140, 161, 182, 208, 235, 269, 303, 345, 389, 442, 497, 564, 634, 718, 806, 910, 1021, 1152, 1290, 1452, 1627, 1828, 2044, 2294

Offset: 0

Jason Kimberley, Feb 22 2011

Number of partitions of n with each part at least 7, and at least 2 parts.

Andrew Howroyd, Table of n, a(n) for n = 0..1000
Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

Disconnected 2-regular simple graphs with girth at least g: A165652 (g=3), A185224 (g=4), A185225 (g=5), A185226 (g=6), this sequence (g=7), A185228 (g=8), A185229 (g=9).
Disconnected k-regular simple graphs with girth at least 7: A185217 (all k), A185207 (triangle); this sequence (k=2), A185237 (k=3).
Cf. A185117, A185327.

Magma
```
A185227 := func;
```

a(n) = A185327() - A185117(n). - Andrew Howroyd, Apr 18 2021

A185217 Number of disconnected regular simple graphs on n vertices with girth at least 7.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 6, 8, 8, 11, 11, 14, 15, 19, 20, 25, 27, 33, 36, 43, 48, 57, 63, 74, 83, 97, 108, 126, 141, 163, 183, 210, 236, 272, 304, 350, 390, 471, 498, 1175, 635, 32957, 807, 1886322, 1022, 101215816, 1291, 5025322391

Offset: 0

Jason Kimberley, Oct 27 2012

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

Disconnected regular graphs with girth at least g: A068932 (g=3), A185214 (g=4), A185215 (g=5), A185216 (g=6), this sequence (g=7).

Disconnected k-regular simple graphs with girth at least 7: this sequence (all k), A185207 (triangle); A185227 (k=2), A185237 (k=3).

A185237 Number of disconnected 3-regular simple graphs on 2n vertices with girth at least 7.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 27, 609, 32237, 1885410, 101214662, 5025320937

Offset: 0

Jason Kimberley, Feb 22 2011

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

Disconnected k-regular simple graphs with girth at least 7: A185217 (all k), A185207 (triangle); A185227 (k=2), this sequence (k=3).

A185200 Square array O(k,g) containing the least nontrivial order of disconnected k-regular simple graphs with girth at least g.

Original entry on oeis.org

6, 8, 8, 10, 12, 10, 12, 16, 20, 12, 14, 20, 38, 28, 14, 16, 24, 60, 52, 48, 16, 18, 28, 80, 84, 134, 60, 18, 20, 32, 100, 124

Offset: 0

Jason Kimberley, Jan 25 2011

This array is twice A054760.

(A proof of the monotonicity with respect to girth appears in Holton & Sheehan)

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

Cf. A185204 - A185207: the triangular arrays D(n,k) counting disconnected k-regular simple graphs with girth at least g on n vertices, for 4 <= g <= 7.

cp's OEIS Frontend

A185227 Number of disconnected 2-regular simple graphs on n vertices with girth at least 7.

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A185217 Number of disconnected regular simple graphs on n vertices with girth at least 7.

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A185237 Number of disconnected 3-regular simple graphs on 2n vertices with girth at least 7.

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A185200 Square array O(k,g) containing the least nontrivial order of disconnected k-regular simple graphs with girth at least g.

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