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.

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

Original entry on oeis.org

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

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   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...
...

Links

Crossrefs

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

Views

Author

Eric W. Weisstein, Jun 27 2017

Keywords

Links

Crossrefs

Main diagonal of A291873.
Cf. A133791, A286139, A287690.

Extensions

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

A369692 Connected domination number of the n X n grid graph.

Original entry on oeis.org

1, 2, 3, 7, 11, 14, 20, 26, 30, 39, 47, 52, 64, 74, 80, 95
Offset: 1

Views

Author

Alexander D. Healy, Feb 25 2024

Keywords

Examples

			From _Andrew Howroyd_, Mar 06 2024: (Start)
a(16) = 95 = 16 + 5*14 + 4*2 + 1.
  . . . . . . . . . . . . . . . .
  X X X X X X X X X X X X X X X X
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X X X
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X X X
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X X X
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X X X
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X X .
(End)

Links

Crossrefs

Cf. A104519, A287690, A302488, A370428.
Cf. A381730 (numbers of minimum connected dominating sets).

Formula

a(3*n) <= n*(3*n+1); a(3*n-1) <= 3*n^2 - 1; a(3*n-2) <= (n-1)*(3*n+1). Conjecturally these inequalities hold with equality for n > 1. - Andrew Howroyd, Mar 06 2024

Extensions

a(10)-a(16) from Andrew Howroyd, Feb 25 2024

A381730 Number of minimum connected dominating sets in the n X n grid graph.

Original entry on oeis.org

1, 4, 2, 16, 126, 24, 800, 16288, 16, 87216, 3554000, 16, 13400336, 882342944, 16, 2376303680
Offset: 1

Views

Author

Eric W. Weisstein, Mar 05 2025

Keywords

Examples

			From _Andrew Howroyd_, Mar 19 2025: (Start)
One of 16 arrangements for a(9):
  . X . . . . . . .
  . X X X X X X X X
  . X . . X . . X .
  . X . . X . . X .
  . X . . X . . X .
  . X . . X . . X .
  . X . . X . . X .
  . X . . X . . X .
  . X . . X . . X .
(End)

Links

Crossrefs

Main diagonal of A381474.
Cf. A287690, A347632.
Cf. A369692 (connected domination numbers).

Formula

a(3*n) = 16 for n >= 3. - Andrew Howroyd, Mar 19 2025

Extensions

a(6)-a(16) from Andrew Howroyd, Mar 19 2025

A360847 Number of dominating induced trees in the n X n grid graph.

Original entry on oeis.org

1, 8, 65, 1280, 78981, 14605388, 7904828158, 12456744197696, 57118103869618858, 760896261783236975004, 29416443122724544970455433, 3297715940113139272931793598648, 1071333966021766251746119497973623975, 1008129126269380724757869194465038817386728
Offset: 1

Views

Author

Andrew Howroyd, Feb 23 2023

Keywords

Comments

A dominating induced tree in a graph is an acyclic connected induced subgraph whose vertices are a dominating set.

Links

  • Eric Weisstein's World of Mathematics, Grid Graph.

Crossrefs

Main diagonal of A360846.
Cf. A287690 (connected dominating sets), A360203 (induced trees).
Showing 1-5 of 5 results.

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