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 1-3 of 3 results.

A302401 Total domination number of the n X n king graph.

Original entry on oeis.org

2, 2, 4, 5, 8, 9, 12, 15, 18, 21, 24, 29, 32, 38, 43, 48, 53, 60, 66, 72, 79
Offset: 2

Views

Author

Eric W. Weisstein, Apr 07 2018

Keywords

Links

Crossrefs

Main diagonal of A303378.
Cf. A303156.

Formula

a(n) ~ n^2/7. - Andrew Howroyd, Apr 22 2018

Extensions

a(17)-a(18) from Andrew Howroyd, Apr 22 2018
a(19)-a(20) from Eric W. Weisstein, Sep 09 2021
a(21) from Eric W. Weisstein, Sep 12 2021
a(22) from Eric W. Weisstein, Sep 15 2021

A303335 Array read by antidiagonals: T(m,n) is the number of minimum total dominating sets in the m X n king graph.

Original entry on oeis.org

0, 1, 1, 2, 6, 2, 1, 9, 9, 1, 1, 4, 8, 4, 1, 4, 8, 1, 1, 8, 4, 3, 89, 3, 35, 3, 89, 3, 1, 56, 76, 9, 9, 76, 56, 1, 2, 16, 17, 1, 1, 1, 17, 16, 2, 9, 64, 1, 130, 9, 9, 130, 1, 64, 9, 4, 780, 6, 16, 60, 8684, 60, 16, 6, 780, 4, 1, 304, 229, 1, 89, 493, 493, 89, 1, 229, 304, 1
Offset: 1

Views

Author

Andrew Howroyd, Apr 21 2018

Keywords

Comments

The minimum size of a total dominating set is the total domination number A303378(m, n).

Examples

			Table begins:
=========================================
m\n| 1  2  3   4  5    6   7   8    9
---+-------------------------------------
1  | 0  1  2   1  1    4   3   1    2 ...
2  | 1  6  9   4  8   89  56  16   64 ...
3  | 2  9  8   1  3   76  17   1    6 ...
4  | 1  4  1  35  9    1 130  16    1 ...
5  | 1  8  3   9  1    9  60  89   45 ...
6  | 4 89 76   1  9 8684 493   1   50 ...
7  | 3 56 17 130 60  493 208  40   32 ...
8  | 1 16  1  16 89    1  40 604    1 ...
9  | 2 64  6   1 45   50  32   1 1192 ...
...

Links

Crossrefs

Rows 1..2 are A302654, A350817.
Main diagonal is A303156.
Cf. A303114, A303293, A303378, A332390, A350815.

A332390 Array read by antidiagonals: T(m,n) is the number of minimal total dominating sets in the m X n king graph.

Original entry on oeis.org

0, 1, 1, 2, 6, 2, 1, 10, 10, 1, 2, 15, 20, 15, 2, 4, 52, 52, 52, 52, 4, 3, 105, 179, 141, 179, 105, 3, 4, 175, 418, 801, 801, 418, 175, 4, 8, 481, 1167, 2950, 7770, 2950, 1167, 481, 8, 9, 1028, 3498, 9792, 34790, 34790, 9792, 3498, 1028, 9, 10, 2000, 9074, 47527, 184318, 204372, 184318, 47527, 9074, 2000, 10
Offset: 1

Views

Author

Andrew Howroyd, Feb 10 2020

Keywords

Examples

			Array begins:
================================================================
m\n | 1   2    3     4       5        6         7          8
----+-----------------------------------------------------------
  1 | 0   1    2     1       2        4         3          4 ...
  2 | 1   6   10    15      52      105       175        481 ...
  3 | 2  10   20    52     179      418      1167       3498 ...
  4 | 1  15   52   141     801     2950      9792      47527 ...
  5 | 2  52  179   801    7770    34790    184318    1305358 ...
  6 | 4 105  418  2950   34790   204372   1593094   14720683 ...
  7 | 3 175 1167  9792  184318  1593094  16260853  231301551 ...
  8 | 4 481 3498 47527 1305358 14720683 231301551 4570906041 ...
  ...

Links

Crossrefs

Rows 1..4 are A302655, A332392, A332393, A332394.
Main diagonal is A332391.
Cf. A286849, A303114, A303118, A303335, A303378.

Formula

T(n,m) = T(m,n).
Showing 1-3 of 3 results.

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

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