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A347922
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Number of minimal total dominating sets in the n X n rook complement graph.
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2
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0, 1, 51, 492, 2500, 8925, 25431, 61936, 134352, 266625, 493075, 861036, 1433796, 2293837, 3546375, 5323200, 7786816, 11134881, 15604947, 21479500, 29091300, 38829021, 51143191, 66552432, 85650000, 109110625, 137697651, 172270476, 213792292, 263338125
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OFFSET
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1,3
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COMMENTS
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The vertex sets which are not totally dominating are just those that are contained in the union of a single row and column. Minimal total dominating sets are:
- any three vertices such that no two are in the same row or column,
- two vertices in each of two rows/columns. (End)
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LINKS
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FORMULA
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a(n) = 6*binomial(n,3)^2 + 2*binomial(n,2)^3 - binomial(n,2)^2.
a(n) = (5*n^2 - 11*n + 5)*n^2*(n-1)^2/12.
G.f.: x*(1 + 44*x + 156*x^2 + 92*x^3 + 7*x^4)/(1 - x)^7.
(End)
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PROG
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(PARI) a(n) = (5*n^2 - 11*n + 5)*n^2*(n-1)^2/12 \\ Andrew Howroyd, Jan 19 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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