|
| |
|
|
A055585
|
|
Second column of triangle A055584.
|
|
5
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| 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.
Index to sequences with linear recurrences with constant coefficients, signature (8,-24,32,-16).
|
|
|
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.
Preceded by 0, this is the binomial transform of the tetrahedral numbers A000292. - Carl Najafi, Sep 08 2011
|
|
|
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 * A099625 A143628 A056279
Adjacent sequences: A055582 A055583 A055584 * A055586 A055587 A055588
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 26 2000
|
| |
|
|
