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A055585
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Second column of triangle A055584.
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5
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1, 6, 25, 88, 280, 832, 2352, 6400, 16896, 43520, 109824, 272384, 665600, 1605632, 3829760, 9043968, 21168128, 49152000, 113311744, 259522560, 590872576, 1337982976, 3014656000, 6761218048, 15099494400, 33587986432, 74440507392
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OFFSET
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0,2
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COMMENTS
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Number of 132-avoiding permutations of [n+5] containing exactly three 123 patterns. - Emeric Deutsch, Jul 13 2001
If X_1,X_2,...,X_n are 2-blocks of a (2n+2)-set X then, for n>=1, a(n-1) is the number of (n+3)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan Janjic, Nov 18 2007
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LINKS
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FORMULA
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G.f.: (1-x)^2/(1-2*x)^4.
a(n) = A055584(n+1, 1). a(n) = sum(a(j), j=0..n-1)+A001793(n+1), n >= 1.
a(n) = 2^(n-3)(n+1)(n+3)(n+8)/3.
Preceded by 0, this is the binomial transform of the tetrahedral numbers A000292. - Carl Najafi, Sep 08 2011
E.g.f.: (1/6)*(2*x^3 + 15*x^2 + 24*x + 6)*exp(2*x). - G. C. Greubel, Aug 22 2015
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EXAMPLE
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a(1)=6 because 432516,432561,435126,452136,532146 and 632145 are the only 132-avoiding permutations of 123456, containing exactly three increasing subsequences of length 3.
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MATHEMATICA
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Table[(1/3)*2^(n-3)*(n+1)*(n+3)*(n+8), {n, 0, 50}] (* G. C. Greubel, Aug 22 2015 *)
LinearRecurrence[{8, -24, 32, -16}, {1, 6, 25, 88}, 30] (* Harvey P. Dale, Nov 03 2017 *)
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PROG
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(PARI) Vec(((1-x)^2)/(1-2*x)^4 + O(x^30)) \\ Michel Marcus, Aug 22 2015
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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