A291873 -id:A291873 - cp's OEIS frontend

A291872 Array read by antidiagonals: T(m,n) = number of connected dominating sets in the grid graph P_m X P_n.

1, 3, 3, 4, 9, 4, 4, 24, 24, 4, 4, 56, 129, 56, 4, 4, 136, 613, 613, 136, 4, 4, 328, 2997, 5617, 2997, 328, 4, 4, 792, 14713, 52955, 52955, 14713, 792, 4, 4, 1912, 72169, 502521, 964755, 502521, 72169, 1912, 4, 4, 4616, 353853, 4763717, 17625829, 17625829, 4763717, 353853, 4616, 4

Offset: 1

Andrew Howroyd, Sep 04 2017

			Array begins:
===============================================================
m\n| 1   2     3       4         5           6             7
---|-----------------------------------------------------------
1  | 1   3     4       4         4           4             4...
2  | 3   9    24      56       136         328           792...
3  | 4  24   129     613      2997       14713         72169...
4  | 4  56   613    5617     52955      502521       4763717...
5  | 4 136  2997   52955    964755    17625829     321381919...
6  | 4 328 14713  502521  17625829   617429805   21550989109...
7  | 4 792 72169 4763717 321381919 21550989109 1436456861467...
...

Andrew Howroyd, Table of n, a(n) for n = 1..435
Eric Weisstein's World of Mathematics, Connected Dominating Set
Eric Weisstein's World of Mathematics, Grid Graph

Row 2 is A291706.
Main diagonal is A287690.
Cf. A218354 (dominating), A287151 (connected).
Cf. A291873 (king).

A289180 Number of connected dominating sets in the n X n king graph.

Original entry on oeis.org

1, 15, 336, 29648, 11293568, 17784998912, 113637188081536, 2924018436019899392, 301641905727809350974464, 124378420721322865523465096192, 204571358406088229163099037060664832, 1340178778197906145868721021815647098466816

Offset: 1

Eric W. Weisstein, Jun 27 2017

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..15
Eric Weisstein's World of Mathematics, Connected Dominating Set
Eric Weisstein's World of Mathematics, King Graph

Main diagonal of A291873.

Cf. A133791, A286139, A287690.

a(6)-a(12) from Andrew Howroyd, Sep 04 2017

A303114 Array read by antidiagonals: T(m,n) = number of total dominating sets in the n X m king graph.

Original entry on oeis.org

0, 1, 1, 3, 11, 3, 4, 47, 47, 4, 5, 165, 353, 165, 5, 9, 625, 2545, 2545, 625, 9, 16, 2435, 19651, 35458, 19651, 2435, 16, 25, 9367, 150719, 538977, 538977, 150719, 9367, 25, 39, 35901, 1149593, 8213971, 16322279, 8213971, 1149593, 35901, 39

Offset: 1

Andrew Howroyd, Apr 18 2018

			Table begins:
============================================================================
m\n|  1    2       3         4           5             6               7
---|------------------------------------------------------------------------
1  |  0    1       3         4           5             9              16 ...
2  |  1   11      47       165         625          2435            9367 ...
3  |  3   47     353      2545       19651        150719         1149593 ...
4  |  4  165    2545     35458      538977       8213971       124153394 ...
5  |  5  625   19651    538977    16322279     496873689     14980146565 ...
6  |  9 2435  150719   8213971   496873689   30158547693   1812834702647 ...
7  | 16 9367 1149593 124153394 14980146565 1812834702647 217221533288240 ...
...

Eric Weisstein's World of Mathematics, King Graph
Eric Weisstein's World of Mathematics, Total Dominating Set

Rows 1..2 are A195971(n-1), A219079.
Main diagonal is A303116.
Cf. A218663 (dominating sets), A291873 (connected dominating sets).
Cf. A303111 (grid graph).

cp's OEIS Frontend

A291872 Array read by antidiagonals: T(m,n) = number of connected dominating sets in the grid graph P_m X P_n.

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A289180 Number of connected dominating sets in the n X n king graph.

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A303114 Array read by antidiagonals: T(m,n) = number of total dominating sets in the n X m king graph.

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Author

Keywords

Examples

Links

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