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!)
A279567 Number of length n inversion sequences avoiding the patterns 100, 110, 120, and 210. 23
1, 1, 2, 6, 21, 82, 343, 1509, 6893, 32419, 156058, 765578, 3815062, 19263736, 98368919, 507197436, 2637242188, 13814247530, 72834238423, 386244387688, 2058933104170, 11026807340592, 59304897232442, 320181600386661, 1734685419170666, 9428340999504441 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i<j<k) such that e_j >= e_k and e_i > e_k. This is the same as the set of length n inversion sequences avoiding 100, 110, 120, and 210.
LINKS
Megan A. Martinez, Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
FORMULA
a(n) ~ c * (1 + sqrt(2))^(2*n) / n^(3/2), where c = 0.066085708825649431003670013119332303648755519420440375... - Vaclav Kotesovec, Oct 07 2021
EXAMPLE
The length 4 inversion sequences avoiding (100, 110, 120, 210) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0101, 0102, 0103, 0111, 0112, 0113, 0121, 0122, 0123.
MAPLE
b:= proc(n, i, m) option remember; `if`(n=0, 1, add((h->
b(n-1, i-h+1, max(m, j)-h))(max(0, min(m-1, j))), j=1..i))
end:
a:= n-> b(n, 1, 0):
seq(a(n), n=0..30); # Alois P. Heinz, Feb 23 2017
MATHEMATICA
b[n_, i_, m_] := b[n, i, m] = If[n == 0, 1, Sum[b[n-1, i-#+1, Max[m, j]-#]& @ Max[0, Min[m-1, j]], {j, 1, i}]]; a[n_] := b[n, 1, 0]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jul 10 2017, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A150219 A150220 A168653 * A281784 A032347 A032346
KEYWORD
nonn
AUTHOR
Megan A. Martinez, Feb 09 2017
EXTENSIONS
a(10)-a(25) from Alois P. Heinz, Feb 23 2017
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 March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)