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.

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

A381474 Array read by antidiagonals: T(m,n) is the number of minimum connected dominating sets in the grid graph P_m X P_n.

Original entry on oeis.org

1, 2, 2, 1, 4, 1, 1, 1, 1, 1, 1, 7, 2, 7, 1, 1, 8, 1, 1, 8, 1, 1, 8, 1, 16, 1, 8, 1, 1, 8, 1, 62, 62, 1, 8, 1, 1, 8, 1, 10, 126, 10, 1, 8, 1, 1, 8, 1, 48, 11, 11, 48, 1, 8, 1, 1, 8, 1, 224, 448, 24, 448, 224, 1, 8, 1, 1, 8, 1, 8, 744, 13, 13, 744, 8, 1, 8, 1
Offset: 1

Views

Author

Andrew Howroyd, Mar 19 2025

Keywords

Examples

			Table begins:
================================================
m\n  | 1 2 3   4    5  6    7     8  9    10 ...
-----+------------------------------------------
   1 | 1 2 1   1    1  1    1     1  1     1 ...
   2 | 2 4 1   7    8  8    8     8  8     8 ...
   3 | 1 1 2   1    1  1    1     1  1     1 ...
   4 | 1 7 1  16   62 10   48   224  8    80 ...
   5 | 1 8 1  62  126 11  448   744  8  1898 ...
   6 | 1 8 1  10   11 24   13    14 15    16 ...
   7 | 1 8 1  48  448 13  800  6408  8  5240 ...
   8 | 1 8 1 224  744 14 6408 16288  8 82128 ...
   9 | 1 8 1   8    8 15    8     8 16     8 ...
  10 | 1 8 1  80 1898 16 5240 82128  8 87216 ...
  ...

Links

Crossrefs

Main diagonal is A381730.
Cf. A291872, A350820, A381475.

Formula

T(m,n) = T(n,m).

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 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.