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.

A360202 Array read by antidiagonals: T(m,n) is the number of (non-null) induced trees in the grid graph P_m X P_n.

Original entry on oeis.org

1, 3, 3, 6, 12, 6, 10, 33, 33, 10, 15, 78, 138, 78, 15, 21, 171, 533, 533, 171, 21, 28, 360, 2003, 3568, 2003, 360, 28, 36, 741, 7453, 23686, 23686, 7453, 741, 36, 45, 1506, 27643, 156614, 277606, 156614, 27643, 1506, 45, 55, 3039, 102432, 1034875, 3234373, 3234373, 1034875, 102432, 3039, 55
Offset: 1

Views

Author

Andrew Howroyd, Feb 22 2023

Keywords

Examples

			Array begins:
=============================================================
m\n|  1   2     3       4        5          6           7 ...
---+---------------------------------------------------------
1  |  1   3     6      10       15         21          28 ...
2  |  3  12    33      78      171        360         741 ...
3  |  6  33   138     533     2003       7453       27643 ...
4  | 10  78   533    3568    23686     156614     1034875 ...
5  | 15 171  2003   23686   277606    3234373    37643572 ...
6  | 21 360  7453  156614  3234373   66136452  1349087217 ...
7  | 28 741 27643 1034875 37643572 1349087217 48136454388 ...
     ...

Links

Crossrefs

Main diagonal is A360203.
Rows 1..2 are A000217, 3*A125128.
Cf. A287151 (connected induced subgraphs), A116469 (spanning trees), A360196 (induced cycles), A360199 (induced paths), A360918 (maximum induced trees).

Formula

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

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).

A360919 Number of maximum induced trees in the n X n grid graph.

Original entry on oeis.org

1, 4, 10, 32, 22, 4120, 488, 65864, 166, 1296, 872, 37652512, 678412, 1858036816, 337856
Offset: 1

Views

Author

Andrew Howroyd, Feb 26 2023

Keywords

Comments

A maximum induced tree is an induced tree of greatest size.

Examples

			The a(3) = 10 maximum induced trees are the following subgraphs and their rotations and reflections.
   O O O    O O O    O O O
   O        O   O      O
   O O O      O O    O O O
.
The a(4) = 32 maximum induced trees are the following subgraphs and their rotations and reflections.
    O O O O    O O O      O O O O    O O   O
    O     O    O   O O      O   O      O O O
    O O   O    O O   O    O O   O    O O   O
    O   O O    O   O O    O   O O    O   O O

Links

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

Crossrefs

Main diagonal of A360918.
Cf. A360203 (induced trees), A360921 (maximum sizes).
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.