A185237 -id:A185237 - 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).

A185036 Number of disconnected 3-regular simple graphs on 2n vertices with girth exactly 6.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 37, 432, 8119, 191254, 4855919, 127937854, 3482858263, 98176518258

Offset: 0

Jason Kimberley, Feb 29 2012

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

Disconnected 3-regular simple graphs with girth exactly g: A185033 (g=3), A185034 (g=4), A185035 (g=5), this sequence (g=6), A185037 (g=7).

a(n) = A185236(n) - A185237(n).

A185207 Triangular array D(n,k) counting disconnected k-regular simple graphs on n vertices with girth at least 7.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 0, 2, 1, 1, 3, 1, 0, 3, 1, 1, 4, 1, 0, 5, 1, 1, 6, 1, 0, 7, 1, 1, 9, 1, 0, 10, 1, 1, 12, 1, 0, 14, 1, 1, 17, 1, 0, 19, 1, 1, 23, 1, 0, 26, 1, 1, 31, 1, 0, 35, 1, 1, 41, 1, 0, 47, 1, 1, 55, 1, 0, 62, 1, 1, 72

Offset: 1

Jason Kimberley, Oct 27 2012

			1: 0;
2: 1;
3: 1;
4: 1, 1;
5: 1, 0;
...
12: 1, 1;
13: 1, 0;
14: 1, 1, 1;
15: 1, 0, 1;
16: 1, 1, 2;
...
47: 1, 0, 235;
48: 1, 1, 269, 1;
...
58: 1, 1, 910, 1885410;
59: 1, 0, 1021, 0;
60: 1, 1, 1152, 101214662;
61: 1, 0, 1290, 0;
62: 1, 1, 1452, 5025320937;

Jason Kimberley, Table of i, a(n)=D(n,k) for i = 1..192 (n = 1..64)
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), this sequence (triangle); A185227 (k=2), A185237 (k=3).

A185037 Number of disconnected 3-regular simple graphs on 2n vertices with girth exactly 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, 101214661, 5025320937

Offset: 0

Jason Kimberley, Feb 29 2012

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

Disconnected 3-regular simple graphs with girth exactly g: A185033 (g=3), A185034 (g=4), A185035 (g=5), A185036 (g=6), this sequence (g=7).

a(n) = A185237(n) - A185238(n).

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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A185036 Number of disconnected 3-regular simple graphs on 2n vertices with girth exactly 6.

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A185207 Triangular array D(n,k) counting disconnected k-regular simple graphs on n vertices with girth at least 7.

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A185037 Number of disconnected 3-regular simple graphs on 2n vertices with girth exactly 7.

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