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 1-4 of 4 results.

A287690 Number of connected dominating sets in the n X n grid graph.

Original entry on oeis.org

1, 9, 129, 5617, 964755, 617429805, 1436456861467, 12128014243816259, 370157141019558632729, 40729998558184127557326187, 16129157077874837008807129310501, 22956060013827748812137293758719842059, 117308080543566432787532732819884994609487361
Offset: 1

Views

Author

Eric W. Weisstein, May 29 2017

Keywords

Links

Crossrefs

Main diagonal of A291872.
Cf. A059525, A133515, A289180.

Extensions

a(6)-a(13) from Andrew Howroyd, Sep 04 2017

A291873 Array read by antidiagonals: T(m,n) = number of connected dominating sets in the m X n king graph.

Original entry on oeis.org

1, 3, 3, 4, 15, 4, 4, 48, 48, 4, 4, 144, 336, 144, 4, 4, 432, 2192, 2192, 432, 4, 4, 1296, 14544, 29648, 14544, 1296, 4, 4, 3888, 96528, 405648, 405648, 96528, 3888, 4, 4, 11664, 640336, 5568336, 11293568, 5568336, 640336, 11664, 4
Offset: 1

Views

Author

Andrew Howroyd, Sep 04 2017

Keywords

Examples

			Array begins:
======================================================================
m\n| 1    2      3        4          5             6               7
---|------------------------------------------------------------------
1  | 1    3      4        4          4             4               4...
2  | 3   15     48      144        432          1296            3888...
3  | 4   48    336     2192      14544         96528          640336...
4  | 4  144   2192    29648     405648       5568336        76414224...
5  | 4  432  14544   405648   11293568     315156544      8793207424...
6  | 4 1296  96528  5568336  315156544   17784998912   1001953789632...
7  | 4 3888 640336 76414224 8793207424 1001953789632 113637188081536...
...

Links

Crossrefs

Row 2 is A188825(n) for n > 2.
Main diagonal is A289180.
Cf. A218663, A291872.

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

A382206 Number of minimum connected dominating sets in the n X n king graph.

Original entry on oeis.org

1, 4, 1, 21, 1, 21, 843, 720, 556841, 99357, 458, 32, 3600, 30580044, 826720, 4
Offset: 1

Views

Author

Eric W. Weisstein, Mar 18 2025

Keywords

Comments

a(1)-a(8) computed with ILP based on a Mathematica implementation by Stan Wagon using an idea from Rob Pratt.

Links

Crossrefs

Cf. A289180, A347554, A381730.
Cf. A370428 (connected domination numbers).

Extensions

a(8)-a(16) from Andrew Howroyd, Mar 19 2025
Showing 1-4 of 4 results.

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

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