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.

A197054 T(n,k)=Number of nXk 0..4 arrays with each element equal to the number of its horizontal and vertical zero neighbors.

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 3, 4, 4, 3, 4, 6, 10, 6, 4, 5, 10, 18, 18, 10, 5, 7, 16, 38, 42, 38, 16, 7, 9, 26, 78, 108, 108, 78, 26, 9, 12, 42, 156, 274, 358, 274, 156, 42, 12, 16, 68, 320, 692, 1132, 1132, 692, 320, 68, 16, 21, 110, 654, 1754, 3580, 4468, 3580, 1754, 654, 110, 21, 28
Offset: 1

Views

Author

R. H. Hardin, Oct 09 2011

Keywords

Comments

Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 0's, every 3 is next to 3 0's, every 4 is next to 4 0's
Also, the number of maximal independent vertex sets in the grid graph P_n X P_k. - Andrew Howroyd, May 16 2017

Examples

			Table starts
..1...2....2.....3......4.......5........7.........9.........12..........16
..2...2....4.....6.....10......16.......26........42.........68.........110
..2...4...10....18.....38......78......156.......320........654........1326
..3...6...18....42....108.....274......692......1754.......4442.......11248
..4..10...38...108....358....1132.....3580.....11382......36270......114992
..5..16...78...274...1132....4468....17742.....70616.....281202.....1117442
..7..26..156...692...3580...17742....88056....439338....2192602....10912392
..9..42..320..1754..11382...70616...439338...2745186...17155374...106972582
.12..68..654..4442..36270..281202..2192602..17155374..134355866..1049189170
.16.110.1326.11248.114992.1117442.10912392.106972582.1049189170.10264692132
...
Some solutions for n=6 k=4
..0..2..1..0....0..2..0..1....2..0..2..0....0..3..0..2....0..2..1..0
..2..0..1..2....1..1..1..1....0..2..1..1....2..0..4..0....3..0..1..2
..1..1..2..0....1..0..2..0....2..1..0..2....1..2..0..2....0..3..1..0
..0..3..0..3....1..1..1..1....0..2..2..0....0..1..1..1....2..0..1..2
..3..0..4..0....0..3..0..2....3..0..1..2....1..1..1..0....1..1..2..0
..0..3..0..2....2..0..3..0....0..2..1..0....1..0..1..1....0..2..0..2

Links

Crossrefs

Column 1 is A000931(n+6).
Column 2 is A006355(n+1).
Columns 3-7 are A197049, A197050, A197051, A197052, A197053.
Main diagonal is A197048.
Cf. A089934 (independent sets), A218354 (dominating sets).

A288956 Number of maximal independent vertex sets (and minimal vertex covers) in the n X n king graph.

Original entry on oeis.org

1, 4, 8, 79, 544, 8197, 201611, 6214593, 391918650, 32239887128, 4599025630995, 1018245217588836, 346578151637999287, 193445218205732588935, 165199496607694525364163, 226636538088997406396236072, 488063150616514603623041818756, 1655950305544572458601638523072809
Offset: 1

Views

Author

Eric W. Weisstein, Jun 20 2017

Keywords

Links

Crossrefs

Main diagonal of A332347.
Cf. A197048 (grid graph), A063443 (independent sets), A193580, A133791 (dominating sets).

Extensions

a(9)-a(18) from Andrew Howroyd, Jun 26 2017

A293177 Triangle read by rows: T(m,n) = number of maximal independent sets in m X n rectangular grid graph (m>=1, 1<=n<=m).

Original entry on oeis.org

1, 2, 2, 2, 4, 10, 3, 6, 18, 42, 4, 10, 38, 108, 358, 5, 16, 78, 274, 1132, 4468, 7, 26, 156, 692, 3580, 17742, 88056, 9, 42, 320, 1754, 11382, 70616, 439338, 2745186, 12, 68, 654, 4442, 36270, 281202, 2192602, 17155374, 16, 110, 1326, 11248, 114992, 1117442, 10912392, 106972582
Offset: 1

Views

Author

N. J. A. Sloane, Oct 19 2017

Keywords

Examples

			Triangle begins:
1,
2,2,
2,4,10,
3,6,18,42,
4,10,38,108,358,
5,16,78,274,1132,4468,
7,26,156,692,3580,17742,88056,
9,42,320,1754,11382,70616,439338,2745186,
12,68,654,4442,36270,281202,2192602,17155374,
16,110,1326,11248,114992,1117442,10912392,106972582,
...

Links

Crossrefs

Main diagonal is A197048.
Rows 3,4,5,6,... form the beginnings of A197049, A197050, A197051, A197052, ..., respectively.
Triangular version of A197054.
Showing 1-3 of 3 results.

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

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