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A055585 Second column of triangle A055584. +0
4
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)
OFFSET

0,2

COMMENT

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

LINKS

Milan Janjic, Two Enumerative Functions

A. Robertson, H. S. Wilf and D. Zeilberger, Permutation patterns and continued fractions, Electr. J. Combin. 6, 1999, #R38.

FORMULA

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.

EXAMPLE

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.

CROSSREFS

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

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 26 2000

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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