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.

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A208039 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 15, 81, 102, 81, 13, 25, 225, 289, 279, 169, 19, 40, 625, 1071, 961, 741, 361, 28, 64, 1600, 3969, 4743, 3249, 1995, 784, 41, 104, 4096, 13230, 23409, 21147, 11025, 5404, 1681, 60, 169, 10816, 44100, 100215, 137641, 94605
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Table starts
..2....4.....6......9......15.......25........40.........64.........104
..4...16....36.....81.....225......625......1600.......4096.......10816
..6...36...102....289....1071.....3969.....13230......44100......153090
..9...81...279....961....4743....23409....100215.....429025.....1942075
.13..169...741...3249...21147...137641....766115....4264225....25232235
.19..361..1995..11025...94605...811801...5866411...42393121...327288437
.28..784..5404..37249..422477..4791721..44918280..421070400..4242161160
.41.1681.14555.126025.1889665.28334329.344414069.4186478209.55078752265

Examples

			Some solutions for n=4 k=3
..0..1..1....0..1..1....1..0..0....1..1..0....1..1..1....1..1..0....1..1..0
..1..0..0....1..1..1....0..0..1....1..0..1....1..1..1....0..1..1....1..0..1
..1..0..0....1..0..1....0..1..1....1..0..0....1..1..1....0..0..1....0..0..1
..0..1..1....0..0..1....1..1..1....1..1..0....1..1..1....1..0..1....0..1..1

Links

Crossrefs

Column 1 is A000930(n+3)
Column 2 is A207170
Column 3 is A208023
Column 4 is A141583(n+3) for n>1
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)
Row 3 is A207704

A303111 Array read by antidiagonals: T(m,n) = number of total dominating sets in the grid graph P_m X P_n.

Original entry on oeis.org

0, 1, 1, 3, 9, 3, 4, 25, 25, 4, 5, 81, 161, 81, 5, 9, 289, 961, 961, 289, 9, 16, 961, 6235, 11236, 6235, 961, 16, 25, 3249, 39601, 137641, 137641, 39601, 3249, 25, 39, 11025, 251433, 1677025, 3270375, 1677025, 251433, 11025, 39
Offset: 1

Views

Author

Andrew Howroyd, Apr 18 2018

Keywords

Comments

Equivalently, the number of n X m binary matrices with every element adjacent to some 0 horizontally or vertically.

Examples

			Table begins:
=======================================================================
m\n|  1    2      3        4          5            6              7
---|-------------------------------------------------------------------
1  |  0    1      3        4          5            9             16 ...
2  |  1    9     25       81        289          961           3249 ...
3  |  3   25    161      961       6235        39601         251433 ...
4  |  4   81    961    11236     137641      1677025       20430400 ...
5  |  5  289   6235   137641    3270375     76405081     1783064069 ...
6  |  9  961  39601  1677025   76405081   3416753209   152598828321 ...
7  | 16 3249 251433 20430400 1783064069 152598828321 13057656650476 ...
...

Links

Crossrefs

Rows 1..2 are A195971(n-1), A141583(n+1).
Main diagonal is A133793.
Cf. A218354 (dominating sets), A291872 (connected dominating sets).
Cf. A303114 (king graph), A303118 (minimal total dominating sets).
Showing 1-2 of 2 results.

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