cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A303156 Number of minimum total dominating sets in the n X n king graph.

Original entry on oeis.org

0, 6, 8, 35, 1, 8684, 208, 604, 1192, 276696, 1362, 2, 2986, 32, 38772, 28520, 441984, 1024, 5047188
Offset: 1

Views

Author

Eric W. Weisstein, Apr 19 2018

Keywords

Links

Crossrefs

Main diagonal of A303335.
Cf. A302401, A303116, A332391.

Extensions

a(6)-a(19) from Andrew Howroyd, Apr 21 2018

A303378 Array read by antidiagonals: T(m,n) = total domination number of the m X n king graph.

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 4, 3, 2, 2, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 6, 5, 4, 6, 6, 6, 6, 4, 5, 6, 6, 6, 5, 6, 7, 8, 7, 6, 5, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 6, 6, 6, 6, 7, 6, 6, 8, 9, 8, 9, 8, 9, 8, 6, 6, 7
Offset: 1

Views

Author

Andrew Howroyd, Apr 22 2018

Keywords

Examples

			Table begins:
=======================================================
m\n| 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16
---+---------------------------------------------------
1  | 1  2  2  2  3  4  4  4  5  6  6  6  7  8  8  8 ...
2  | 2  2  2  2  3  4  4  4  5  6  6  6  7  8  8  8 ...
3  | 2  2  2  2  3  4  4  4  5  6  6  6  7  8  8  8 ...
4  | 2  2  2  4  4  4  6  6  6  8  8  8 10 10 10 12 ...
5  | 3  3  3  4  5  6  7  8  9 10 11 12 13 14 15 16 ...
6  | 4  4  4  4  6  8  8  8 10 12 12 12 14 16 16 16 ...
7  | 4  4  4  6  7  8  9 10 11 12 14 14 16 17 18 19 ...
8  | 4  4  4  6  8  8 10 12 12 14 16 16 18 20 20 22 ...
9  | 5  5  5  6  9 10 11 12 15 16 17 18 21 22 23 24 ...
...

Links

Crossrefs

Main diagonal is A302401.
Cf. A300358, A303114, A303335.

A303116 Number of total dominating sets in the n X n king graph.

Original entry on oeis.org

0, 11, 353, 35458, 16322279, 30158547693, 217221533288240, 6223220939472363571, 709791800918008570287847, 321673400252458591521699180612, 579292884621843116328602359172702605, 4146239141804826663870561644604700888044071
Offset: 1

Views

Author

Andrew Howroyd, Apr 18 2018

Keywords

Links

Crossrefs

Main diagonal of A303114.
Cf. A133791, A302401, A303156, A332391.

A332391 Number of minimal total dominating sets in the n X n king graph.

Original entry on oeis.org

0, 6, 20, 141, 7770, 204372, 16260853, 4570906041, 1437642613959, 1151580438927120
Offset: 1

Views

Author

Andrew Howroyd, Feb 10 2020

Keywords

Links

Crossrefs

Main diagonal of A332390.
Cf. A302401, A303116, A303156.

Extensions

a(9)-a(10) from Christian Sievers, Dec 02 2023

A370428 Connected domination number of the n X n king graph.

Original entry on oeis.org

1, 1, 1, 4, 5, 8, 12, 15, 20, 24, 28, 33, 39, 46, 52, 58
Offset: 1

Views

Author

Alexander D. Healy, Feb 24 2024

Keywords

Comments

In other words, a(n) is the minimum number of kings that can be placed on an n X n chessboard such that (i) the occupied squares form a single connected component, and (ii) every square is either occupied by a king or adjacent to one that is.
a(17) <= 67; a(18) <= 75; a(19) <= 83; a(20) <= 92.

Links

Crossrefs

Cf. A075561, A289180, A302401, A369692.
Cf. A382206 (numbers of minimum connected dominating sets).

Extensions

a(13)-a(16) from Andrew Howroyd, Feb 25 2024
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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