A076328 -id:A076328 - cp's OEIS frontend

A084269 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes having chromatic number k, 1 <= k <= n.

1, 0, 1, 0, 1, 1, 0, 3, 2, 1, 0, 5, 12, 3, 1, 0, 17, 64, 26, 4, 1, 0, 44, 475, 282, 46, 5, 1, 0, 182, 5036, 5009, 809, 74, 6, 1, 0, 730, 80947, 149551, 27794, 1940, 110, 7, 1, 0, 4032, 2010328, 7694428, 1890221, 113272, 4125, 156, 8, 1, 0, 25598, 76115143, 667036310, 248580644, 14545025, 389583, 8040, 212, 9, 1

Offset: 0

Eric W. Weisstein, May 24 2003

			Triangle begins:
  1;
  0,   1;
  0,   1,     1;
  0,   3,     2,      1;
  0,   5,    12,      3,     1;
  0,  17,    64,     26,     4,    1;
  0,  44,   475,    282,    46,    5,   1;
  0, 182,  5036,   5009,   809,   74,   6, 1;
  0, 730, 80947, 149551, 27794, 1940, 110, 7, 1;
  ...

Eric Weisstein's World of Mathematics, n-Chromatic Graph

Row sums are A001349.
Columns k=3..7 are A126737, A126738, A126739, A126740, A241702.
Partial row sums include A005142, A076322, A076323, A076324, A076325, A076326, A076327, A076328.
Essentially the same table as A126736.
Cf. A084268 (not necessarily connected), A115597.

a(37)-a(66) from Andrew Howroyd, Dec 02 2018

A076322 Number of connected 3-colorable (i.e., chromatic number <= 3) simple graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 5, 17, 81, 519, 5218, 81677, 2014360, 76140741, 4303246908

Offset: 1

Eric W. Weisstein, Oct 06 2002

Maria Chudnovsky, Jan Goedgebeur, Oliver Schaudt, Mingxian Zhong, Obstructions for three-coloring graphs without induced paths on six vertices, arXiv preprint, arXiv:1504.06979 [math.CO], 2015-2018.
Eric Weisstein's World of Mathematics, n-Colorable Graph

Cf. A005142, A076323, A076324, A076325, A076326, A076327, A076328.

Cf. A076279, A076315, A084269, A126737.

A076315 = Cases[Import["https://oeis.org/A076315/b076315.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
EulerInvTransform[A076315] (* Jean-François Alcover, Sep 25 2019, updated Mar 17 2020 *)

Inverse Euler transform of A076315. - Andrew Howroyd, Dec 02 2018

a(10)-a(11) from Andrew Howroyd, Dec 02 2018

a(12) from Jinyuan Wang, Feb 23 2020

A076323 Number of connected 4-colorable (i.e., chromatic number <= 4) simple graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 6, 20, 107, 801, 10227, 231228, 9708788, 743177051, 100580560531

Offset: 1

Eric W. Weisstein, Oct 06 2002

Maria Chudnovsky, Jan Goedgebeur, Oliver Schaudt, Mingxian Zhong, Obstructions for three-coloring graphs without induced paths on six vertices, arXiv preprint, arXiv:1504.06979 [math.CO], 2015-2018.
Eric Weisstein's World of Mathematics, n-Colorable Graph

Cf. A005142, A076322, A076324, A076325, A076326, A076327, A076328.

Cf. A076280, A076316, A084269, A126738.

A076316 = Cases[Import["https://oeis.org/A076316/b076316.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
EulerInvTransform[A076316] (* Jean-François Alcover, Sep 25 2019, updated Mar 17 2020 *)

Inverse Euler transform of A076316. - Andrew Howroyd, Dec 02 2018

a(10)-a(11) from Andrew Howroyd, Dec 02 2018

a(12) from Sean A. Irvine, Apr 13 2025

A076324 Number of connected 5-colorable (i.e., chromatic number <= 5) simple graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 6, 21, 111, 847, 11036, 259022, 11599009, 991757695

Offset: 1

Eric W. Weisstein, Oct 06 2002

Eric Weisstein's World of Mathematics, k-Colorable Graph

Cf. A005142, A076322, A076323, A076325, A076326, A076327, A076328.

Cf. A076281, A076317, A084269, A126739.

Inverse Euler transform of A076317. - Andrew Howroyd, Dec 02 2018

a(10)-a(11) from Andrew Howroyd, Dec 02 2018

A076325 Number of connected 6-colorable (i.e., chromatic number <= 6) simple graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 6, 21, 112, 852, 11110, 260962, 11712281, 1006302720

Offset: 1

Eric W. Weisstein, Oct 06 2002

Eric Weisstein's World of Mathematics, n-Colorable Graph

Cf. A005142, A076322, A076323, A076324, A076326, A076327, A076328.

Cf. A076282, A076318, A084269, A126740.

Inverse Euler transform of A076318. - Andrew Howroyd, Dec 02 2018

a(10)-a(11) from Andrew Howroyd, Dec 02 2018

A076326 Number of connected 7-colorable (i.e., chromatic number <= 7) simple graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 6, 21, 112, 853, 11116, 261072, 11716406, 1006692303

Offset: 1

Eric W. Weisstein, Oct 06 2002

Eric Weisstein's World of Mathematics, n-Colorable Graph

Cf. A005142, A076322, A076323, A076324, A076325, A076327, A076328.

Cf. A076283, A076319, A084269, A241702.

Inverse Euler transform of A076319. - Andrew Howroyd, Dec 02 2018

a(10)-a(11) from Andrew Howroyd, Dec 02 2018

A076327 Number of connected 8-colorable (i.e., chromatic number <= 8) simple graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 6, 21, 112, 853, 11117, 261079, 11716562, 1006700343

Offset: 1

Eric W. Weisstein, Oct 06 2002

Eric Weisstein's World of Mathematics, n-Colorable Graph

Cf. A005142, A076322, A076323, A076324, A076325, A076326, A076328.

Cf. A205567, A076320, A084269.

Inverse Euler transform of A076320. - Andrew Howroyd, Dec 02 2018

a(10)-a(11) from Andrew Howroyd, Dec 02 2018

cp's OEIS Frontend

A084269 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes having chromatic number k, 1 <= k <= n.

Views

Author

Keywords

Examples

Links

Crossrefs

Extensions

A076322 Number of connected 3-colorable (i.e., chromatic number <= 3) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A076323 Number of connected 4-colorable (i.e., chromatic number <= 4) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A076324 Number of connected 5-colorable (i.e., chromatic number <= 5) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions

A076325 Number of connected 6-colorable (i.e., chromatic number <= 6) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions

A076326 Number of connected 7-colorable (i.e., chromatic number <= 7) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions

A076327 Number of connected 8-colorable (i.e., chromatic number <= 8) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions