A231888
Number of maximal 3-independent sets in the 3-dimensional (3, 3, n) grid graph.
Original entry on oeis.org
0, 7, 26, 57, 190, 646, 1914, 5960, 18824, 58248, 181196, 565328, 1759720, 5477376, 17062956, 53131824, 165443096, 515219344, 1604410136, 4996129756, 15558217340, 48448930636, 150871392396, 469819443204, 1463035474136, 4555944690588, 14187380873768
Offset: 0
- Andrew Howroyd, Table of n, a(n) for n = 0..100
- R. Euler, P. Oleksik, Z. Skupien, Counting Maximal Distance-Independent Sets in Grid Graphs, Discussiones Mathematicae Graph Theory. Volume 33, Issue 3, Pages 531-557, ISSN (Print) 2083-5892, July 2013; see also.
A197053
Number of nX7 0..4 arrays with each element equal to the number its horizontal and vertical zero neighbors.
Original entry on oeis.org
7, 26, 156, 692, 3580, 17742, 88056, 439338, 2192602, 10912392, 54394628, 271160024, 1351103246, 6733077562, 33557756016, 167232569172, 833404135538, 4153405692526, 20698773896328, 103153449929238, 514074952403758
Offset: 1
Some solutions for n=4
..0..2..1..0..1..2..0....0..1..1..1..0..3..0....0..2..0..3..0..3..0
..3..0..2..1..2..0..3....1..2..0..1..3..0..2....1..1..2..0..4..0..3
..0..4..0..3..0..4..0....2..0..3..1..0..2..1....2..0..2..2..0..4..0
..2..0..3..0..3..0..2....0..3..0..1..1..1..0....0..3..0..1..2..0..2
A231882
Number of maximal 2-independent sets in the planar 3 X n grid graph.
Original entry on oeis.org
0, 3, 4, 11, 17, 36, 69, 133, 254, 499, 959, 1852, 3589, 6943, 13410, 25951, 50197, 97050, 187699, 363047, 702066, 1357755, 2625947, 5078438, 9821417, 18994465, 36734648, 71043261, 137395463, 265718350, 513889567, 993844901, 1922062694, 3717202293, 7188941039
Offset: 0
- Andrew Howroyd, Table of n, a(n) for n = 0..200
- R. Euler, P. Oleksik, Z. Skupien, Counting Maximal Distance-Independent Sets in Grid Graphs, Discussiones Mathematicae Graph Theory. Volume 33, Issue 3, Pages 531-557, ISSN (Print) 2083-5892, July 2013; see also.
- Index entries for linear recurrences with constant coefficients, signature (1,0,3,1,0,1,-2,0,-1).
-
LinearRecurrence[{1,0,3,1,0,1,-2,0,-1},{0,3,4,11,17,36,69,133,254,499},40] (* Harvey P. Dale, Oct 05 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
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,
...
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