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A332347
Array read by antidiagonals: T(m,n) is the number of maximal independent sets in the m X n king graph.
5
1, 2, 2, 2, 4, 2, 3, 6, 6, 3, 4, 12, 8, 12, 4, 5, 20, 22, 22, 20, 5, 7, 36, 40, 79, 40, 36, 7, 9, 64, 82, 194, 194, 82, 64, 9, 12, 112, 176, 537, 544, 537, 176, 112, 12, 16, 200, 340, 1519, 1882, 1882, 1519, 340, 200, 16, 21, 352, 722, 4011, 6490, 8197, 6490, 4011, 722, 352, 21
OFFSET
1,2
COMMENTS
Also the number of minimal vertex covers in the m X n king graph.
LINKS
Eric Weisstein's World of Mathematics, King Graph
Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set
Eric Weisstein's World of Mathematics, Minimal Vertex Cover
FORMULA
T(n,m) = T(m,n).
EXAMPLE
Array begins:
=====================================================
m\n | 1 2 3 4 5 6 7 8
----+------------------------------------------------
1 | 1 2 2 3 4 5 7 9 ...
2 | 2 4 6 12 20 36 64 112 ...
3 | 2 6 8 22 40 82 176 340 ...
4 | 3 12 22 79 194 537 1519 4011 ...
5 | 4 20 40 194 544 1882 6490 20534 ...
6 | 5 36 82 537 1882 8197 36301 144409 ...
7 | 7 64 176 1519 6490 36301 201611 1009321 ...
8 | 9 112 340 4011 20534 144409 1009321 6214593 ...
...
CROSSREFS
Rows 1..4 are A000931(n+6), A107383(n+2), A332348, A332349.
Main diagonal is A288956.
Cf. A197054 (grid graph), A218663 (dominating sets), A245013 (independent sets), A286849 (minimal dominating sets).
Sequence in context: A066761 A108920 A079405 * A201353 A072048 A161841
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Feb 10 2020
STATUS
approved