login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A165541 Number of permutations of length n which avoid the patterns 4213 and 3142. 0
1, 2, 6, 22, 89, 379, 1664, 7460, 33977, 156727, 730619, 3436710, 16291842, 77758962, 373369867, 1802399037, 8742691627, 42590945206, 208300979739, 1022385319050, 5034470059883, 24865173540949, 123147075005750 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
M. H. Albert, M. D. Atkinson, and V. Vatter, Inflations of geometric grid classes: three case studies, arXiv:1209.0425 [math.CO], 2012.
Christian Bean, Finding structure in permutation sets, Ph.D. Dissertation, Reykjavík University, School of Computer Science, 2018.
Darla Kremer and Wai Chee Shiu, Finite transition matrices for permutations avoiding pairs of length four patterns, Discrete Math. 268 (2003), 171-183. MR1983276 (2004b:05006). See Table 1.
FORMULA
G.f. f satisfies: x^3*f^6+(7*x^3-7*x^2+2*x)*f^5+(x^4+14*x^3-21*x^2+10*x-1)*f^4+(4*x^4+8*x^3-19*x^2+11*x-2)*f^3+(6*x^4-5*x^3-2*x^2+2*x)*f^2+(4*x^4-7*x^3+4*x^2-x)*f+x^4-2*x^3+x^2 = 0.
EXAMPLE
There are 22 permutations of length 4 which avoid these two patterns, so a(4)=22.
MATHEMATICA
f = 0; m = 24;
Do[f = -(1/(x(4x^3 - 7x^2 + 4x - 1)))(x^3 f^6 + x(7x^2 - 7x + 2) f^5 + (x^4 + 14x^3 - 21x^2 + 10x - 1) f^4 + (1 - 2x)^2 (x^2 + 3x - 2) f^3 + x(6 x^3 - 5x^2 - 2x + 2) f^2 + (x-1)^2 x^2) + O[x]^m, {m}];
CoefficientList[f/x, x] (* Jean-François Alcover, Feb 17 2019 *)
CROSSREFS
Sequence in context: A165540 A363809 A111053 * A165542 A165543 A049123
KEYWORD
nonn
AUTHOR
Vincent Vatter, Sep 21 2009
EXTENSIONS
Reference corrected by Vincent Vatter, Sep 04 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 26 18:12 EDT 2024. Contains 373720 sequences. (Running on oeis4.)