cp's OEIS Frontend

A279562 Number of length n inversion sequences avoiding the patterns 100, 102, and 201.

%I A279562 #24 Jun 08 2025 15:19:21
%S A279562 1,1,2,6,21,78,299,1176,4729,19378,80667,340260,1451277,6248758,
%T A279562 27124703,118576648,521574769,2306766426,10251761219,45759404076,
%U A279562 205050758165,922104978430,4160045001703,18823187479504,85400356099001,388422301113250,1770695668597643,8089198184655732,37027394471695197
%N A279562 Number of length n inversion sequences avoiding the patterns 100, 102, and 201.
%C A279562 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_i > e_j <= e_k and e_i <> e_k. This is the same as the set of length n inversion sequences avoiding 100, 102, and 201.
%H A279562 Nathan J. Britt, <a href="/A279562/b279562.txt">Table of n, a(n) for n = 0..1000</a>
%H A279562 Megan A. Martinez, Carla D. Savage, <a href="https://arxiv.org/abs/1609.08106">Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations</a>, arXiv:1609.08106 [math.CO], 2016-2018.
%F A279562 G.f.: (2 + x - 10*x^2 + 4*x^3 - (2-3*x)*(1 - 4*x - 4*x^2)^(1/2)) / (8*x*(1 - x)^2). - _Nathan J. Britt_, Jun 08 2025
%F A279562 a(n) ~ c * (2 + 2*sqrt(2))^n / n^(3/2), where c = 0.40413545332026258682681691461076303199449216224437... - _Nathan J. Britt_, Jun 08 2025
%e A279562 The length 4 inversion sequences avoiding (100, 102, 201) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0101, 0110, 0111, 0112, 0113, 0120, 0121, 0122, 0123.
%Y A279562 Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.
%K A279562 nonn
%O A279562 0,3
%A A279562 _Megan A. Martinez_, Feb 09 2017
%E A279562 a(10)-a(12) from _Alois P. Heinz_, Feb 24 2017
%E A279562 a(13)-a(17) from _Bert Dobbelaere_, Dec 30 2018
%E A279562 More terms from _Nathan J. Britt_, Jun 08 2025