A288721 -id:A288721 - cp's OEIS frontend

A287064 Number of dominating sets in the n-triangular grid graph.

1, 7, 45, 685, 20409, 1201941, 141147379, 32952001519, 15299378914117, 14127550190798059, 25944752255914338751, 94759724685920514675099, 688318811614248548827285461, 9943676783895971991257124086453, 285690558616920990681823749334591359, 16324365307318944099676240468111164604873

Offset: 0

Eric W. Weisstein, May 19 2017

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..20
Eric Weisstein's World of Mathematics, Dominating Set
Eric Weisstein's World of Mathematics, Triangular Grid Graph

Cf. A251419, A288721, A297572, A303049.

a(7)-a(11) from Andrew Howroyd, May 21 2017

Terms a(12) and beyond from Andrew Howroyd, Apr 18 2018

A303049 Number of total dominating sets in the n-triangular grid graph.

Original entry on oeis.org

4, 32, 370, 10102, 547888, 57177700, 11840492228, 4851988794700, 3925043687686610, 6272313979455281150, 19802247395866119585902, 123501868366552999691029394, 1521619453753652011100192319196, 37035171896737433898000971545353724, 1780729821252117006470518879967287810584

Offset: 1

Eric W. Weisstein, Apr 17 2018

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..19
Eric Weisstein's World of Mathematics, Total Dominating Set
Eric Weisstein's World of Mathematics, Triangular Grid Graph

Cf. A287064, A288721, A302486.

Terms a(6) and beyond from Andrew Howroyd, Apr 17 2018

A288722 Number of connected (non-null) inducted subgraphs in the n-triangular grid graph.

Original entry on oeis.org

1, 7, 47, 492, 10030, 415504, 34821705, 5873737591, 1986293769719, 1342287826603144, 1808263364071413240, 4847274244238104590520, 25819608749278516743821755, 272991106439478141199607596649, 5724287949499035173796596544768241, 237885203520333624684917852305536258876

Offset: 1

Eric W. Weisstein, Jun 14 2017

Andrew Howroyd, Table of n, a(n) for n = 1..20
Eric Weisstein's World of Mathematics, Triangular Grid Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph

Cf. A288721.

a(8) onwards from Andrew Howroyd, Aug 15 2017

A297572 Number of minimum dominating sets in the n-triangular grid graph.

Original entry on oeis.org

1, 3, 6, 26, 2, 75, 89, 18, 108, 4, 9042, 10265, 10524, 138, 8, 72, 596, 4438, 390, 16, 55716

Offset: 0

Eric W. Weisstein, Dec 31 2017

Eric Weisstein's World of Mathematics, Minimum Dominating Set
Eric Weisstein's World of Mathematics, Triangular Grid Graph

Cf. A251419, A287064, A288721.

a(8)-a(10) from Andrew Howroyd, Jan 02 2018

Offset corrected and a(11)-a(20) from Andrew Howroyd, May 19 2018

A373393 Number of minimum connected dominating sets in the n-triangular grid graph.

Original entry on oeis.org

1, 3, 3, 11, 32, 48, 16, 48, 15072, 9552, 192, 333216, 134880, 6570096, 768, 9748704, 70272

Offset: 0

Eric W. Weisstein, Jun 03 2024

The connected domination number is A379353(n).

			One of 16 arrangements for a(6) with 10 vertices:
              o
            o   X
          o   X   o
        o   o   X   o
      o   X   X   o   o
    X   X   o   X   X   o
  o   o   o   o   o   X   o

Eric Weisstein's World of Mathematics, Connected Dominating Set.
Eric Weisstein's World of Mathematics, Triangular Grid Graph.
Eric W. Weisstein, Triangular Grid Graph Connected Dominating Sets.

Cf. A288721, A379353.

a(7)-a(16) from Andrew Howroyd, Dec 25 2024

A379353 Connected domination number of the n-triangular grid graph.

Original entry on oeis.org

1, 1, 2, 4, 6, 8, 10, 13, 17, 20, 23, 28, 32, 37, 41, 47, 52

Offset: 0

Andrew Howroyd, Dec 27 2024

Eric Weisstein's World of Mathematics, Connected Domination Number.
Eric Weisstein's World of Mathematics, Triangular Grid Graph.

Cf. A251419, A288721, A373393.

a(n) >= floor((n^2 + 3*n + 10)/6) for n >= 3.

a(n) ~ n^2/6.

cp's OEIS Frontend

A287064 Number of dominating sets in the n-triangular grid graph.

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A303049 Number of total dominating sets in the n-triangular grid graph.

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A288722 Number of connected (non-null) inducted subgraphs in the n-triangular grid graph.

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A297572 Number of minimum dominating sets in the n-triangular grid graph.

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A373393 Number of minimum connected dominating sets in the n-triangular grid graph.

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A379353 Connected domination number of the n-triangular grid graph.

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