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A269889
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The number of permutations of 1, 2,..., n such that none of 123, 132, 213, 231, 312, 321 appear in the permutation.
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0
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1, 1, 2, 0, 12, 84, 576, 4320, 36000, 332640, 3386880, 37739520, 457228800, 5987520000, 84304281600, 1270312243200, 20399720140800, 347841381888000, 6276836966400000, 119510975840256000, 2394487765942272000, 50361071569256448000, 1109403315728547840000
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = n! - 6(n-2)! for n>=3.
-(n+1)*(n-4)*a(n) +(n-2)*(n-3)*(n+2)*a(n-1)=0 for n>=4 - R. J. Mathar, Nov 07 2017
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EXAMPLE
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There are 12 ways that permutations of 4 can have 1, 2, and 3 together. They are: 1234, 1324, 2134, 2314, 3124, 3214, 4123, 4132, 4213, 4231, 4312, 4321. Since there are 24 permutations, a(4) = 24-12 = 12
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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