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Search: id:A134362
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| A134362 |
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a(n) is the number of functions f:X->X, where |X| = n, such that for every x in X, f(f(x))<>x (i.e. the square of the function has no fixed points, note this implies that the function has no fixed points). |
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+0
1
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| 0, 0, 2, 30, 444, 7360, 138690, 2954364, 70469000, 1864204416
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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This sequence arose when analyzing the Zen Stare game. This game is played with a group of people standing in a circle. They start heads bowed and then everyone raises their heads simultaneously and looks at someone else in the circle. If no two people are looking at each other a Zen Stare is achieved.
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FORMULA
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see Maple code
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EXAMPLE
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a(3) = 2 because given a three element set X:= {A, B, C} the only functions whose square has no fixed points are f:X->X where f(A)=B, f(B)=C, f(C)=A and g:X->X where g(A)=C, g(B)=A, g(C)=B
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MAPLE
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a:= n -> (n-1)^n + sum((-1)^i*product(binomial(n-2*(j-1), 2), j=1..i)*(n-1)^(n-2*i)/i!, i=1..floor(n/2));
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CROSSREFS
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Sequence in context: A091345 A077517 A060042 this_sequence A143414 A099046 A020547
Adjacent sequences: A134359 A134360 A134361 this_sequence A134363 A134364 A134365
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KEYWORD
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nonn
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AUTHOR
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Adam Day (adam.r.day(AT)gmail.com), Jan 17 2008
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