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Search: id:A035287
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| A035287 |
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Number of ways to place a non-attacking white and black rook on n X n chessboard. |
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+0
2
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| 0, 4, 36, 144, 400, 900, 1764, 3136, 5184, 8100, 12100, 17424, 24336, 33124, 44100, 57600, 73984, 93636, 116964, 144400, 176400, 213444, 256036, 304704, 360000, 422500, 492804, 571536, 659344, 756900, 864900, 984064, 1115136, 1258884
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) is equal to the number of functions f:{1,2,3,4}->{1,2,...,n} such that for fixed different x_1, x_2 in {1,2,3,4} and fixed y_1, y_2 in {1,2,...,n} we have f(x_1)<>y_1 and f(x_2)<>y_2. - Milan R. Janjic (agnus(AT)blic.net), Apr 17 2007
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LINKS
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Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
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Diagonal of [A132710]*Transpose[A132710]. - Tom Copeland (tcjpn(AT)msn.com), Nov 20 2007
a(n) = n^2 (n-1)^2
a(n) = A002378(n)^2. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 11 2006
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EXAMPLE
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There are 36 ways of putting 2 distinct rooks on 3 X 3 so that neither can capture the other
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MAPLE
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seq((numbperm (n, 2))^2, n=1..34); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007
a:=n->sum(sum(n^2, j=0..n), k=0..n): seq(a(n), n=0..33); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
a:=n->sum(sum (2*binomial(n, 2), j=2..n), k=1..n): seq(a(n), n=1..34); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 02 2007
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CROSSREFS
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Cf. A002378.
Sequence in context: A045490 A060783 A125756 this_sequence A083223 A102263 A103931
Adjacent sequences: A035284 A035285 A035286 this_sequence A035288 A035289 A035290
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KEYWORD
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nonn
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AUTHOR
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Erich Friedman (erich.friedman(AT)stetson.edu)
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