A185218 -id:A185218 - cp's OEIS frontend

A185318 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 8.

1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 3, 2, 3, 2, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 9, 8, 11, 11, 14, 14, 19, 18, 23, 24, 30, 31, 41, 40, 61, 52, 217, 67, 4416, 86, 266463, 111, 20807816, 141

Offset: 0

Jason Kimberley, Dec 18 2012

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

Not necessarily connected regular simple graphs with girth at least g: A005176 (g=3), A185314 (g=4), A185315 (g=5), A185316 (g=6), A185317 (g=7), this sequence (g=8), A185319 (g=9).

a(n) = A186728(n) + A185218(n).

A185219 Number of disconnected regular simple graphs on n vertices with girth at least 9.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 7, 9, 9, 12, 12, 15, 16, 19, 20, 25, 26, 31, 34, 40, 43, 51, 55, 64, 71, 81, 89, 103, 113, 129, 143, 162, 179, 204, 225, 254, 282, 317, 351, 396, 437, 490, 544, 608, 673, 753, 832, 928, 1028, 1144, 1264

Offset: 0

Jason Kimberley, Dec 19 2012

			a(116) = 89574 because there is 1 such 0-regular graph (116 disconnected vertices), 1 such 1-regular graph (58 loose edges), A185229(116) = 89401, and 171 such 3-regular graphs (because A210709(58)=18).

Jason Kimberley, Table of n, a(n) for n = 0..116
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), A185217 (g=7), A185218 (g=8), this sequence (g=9).

A210718 Number of disconnected regular simple graphs on n vertices with girth exactly 8.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 7, 7, 9, 10, 12, 13, 16, 17, 21, 23, 27, 30, 36, 39, 46, 51, 60, 66, 77, 85, 99, 110, 126, 140, 162, 179, 205, 228, 261, 289, 329, 365, 416, 461, 524, 579, 669, 726, 976, 909, 5378, 1134

Offset: 0

Jason Kimberley, Dec 19 2012

Jason Kimberley, Table of n, a(n) for n = 0..77
Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth exactly g

a(n) = A185218(n) - A185219(n).

A210717 Number of disconnected regular simple graphs on n vertices with girth exactly 7.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 8, 10, 11, 13, 15, 18, 20, 24, 27, 32, 36, 42, 48, 56, 63, 73, 83, 96, 109, 125, 144, 162, 210, 209, 845, 270, 32541, 346, 1885800, 443, 101215159, 565, 5025321572

Offset: 0

Jason Kimberley, Dec 18 2012

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

a(n) = A185217(n) - A185218(n).

cp's OEIS Frontend

A185318 Number of, not necessarily connected, regular simple graphs on n vertices with girth at least 8.

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A185219 Number of disconnected regular simple graphs on n vertices with girth at least 9.

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A210718 Number of disconnected regular simple graphs on n vertices with girth exactly 8.

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Author

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A210717 Number of disconnected regular simple graphs on n vertices with girth exactly 7.

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Author

Keywords

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Formula