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A291593
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Number of (non-null) connected induced subgraphs in the n X n rook complement graph.
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2
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1, 6, 397, 64627, 33548446, 68719441230, 562949953224709, 18446744073708514623, 2417851639229258344134994, 1267650600228229401496677070990, 2658455991569831745807614120434011325, 22300745198530623141535718272648360902487971
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OFFSET
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1,2
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COMMENTS
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The vertex sets inducing disconnected subgraphs are:
- two or more vertices taken from a single row or column,
- any vertex combined with at least one from the same row and at least one from the same column,
- four vertices forming the corners of a rectangle. (End)
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LINKS
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FORMULA
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a(n) = 2^(n^2) - 2*n*(2^n-n-1) - n^2*(2^(n-1)-1)^2 - binomial(n,2)^2 - 1. - Andrew Howroyd, Aug 30 2017
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MATHEMATICA
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Table[2^(n^2) - 2 n (2^n - n - 1) - n^2 (2^(n - 1) - 1)^2 - Binomial[n, 2]^2 - 1, {n, 10}]
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PROG
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(PARI) a(n) = 2^(n^2) - 2*n*(2^n-n-1) - n^2*(2^(n-1)-1)^2 - binomial(n, 2)^2 - 1; \\ Andrew Howroyd, Aug 30 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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