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Search: id:A055585
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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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of 132-avoiding permutations of [n+5] containing exactly three 123 patterns. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 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 R. Janjic (agnus(AT)blic.net), Nov 18 2007
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LINKS
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Milan Janjic, Two Enumerative Functions
A. Robertson, H. S. Wilf and D. Zeilberger, Permutation patterns and continued fractions, Electr. J. Combin. 6, 1999, #R38.
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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.
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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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CROSSREFS
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Cf. A055584, partial sums of A049612, n >= 1.
Sequence in context: A166814 A133714 A164271 this_sequence A099625 A143628 A056279
Adjacent sequences: A055582 A055583 A055584 this_sequence A055586 A055587 A055588
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 26 2000
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