cp's OEIS Frontend

A061061 Maximal number of 132 patterns in a permutation of 1,2,...,n.

%I A061061 #20 Aug 01 2018 19:04:17
%S A061061 0,0,1,3,6,12,20,31,46,64,87,115,147,186,231,282,342,408,482,566,657,
%T A061061 759,871,991,1126,1270,1424,1594,1774,1968,2177,2397,2635,2887,3151,
%U A061061 3436,3735,4050,4386,4736,5106,5496,5901,6330,6778,7244,7737,8247,8778,9336
%N A061061 Maximal number of 132 patterns in a permutation of 1,2,...,n.
%C A061061 a(n) = A216499(n) - (n choose 3). lim_{n --> infinity} a(n) / n^3 = (2 sqrt(3) - 3) / 6 = 0.077350... a(n) / n^3 < (2 sqrt(3) - 3) / 6 = 0.077350... for all n > 0. [Chao et al. (2012)]. - _Jesper Jansson_, Sep 10 2012
%D A061061 K.-M. Chao, A.-C. Chu, J. Jansson, R. S. Lemence, and A. Mancheron. Asymptotic Limits of a New Type of Maximization Recurrence with an Application to Bioinformatics. Proceedings of the Ninth Annual Conference on Theory and Applications of Models of Computation (TAMC 2012), Lecture Notes in Computer Science, Vol. 7287, pp. 177-188, Springer-Verlag Berlin Heidelberg, 2012.
%D A061061 W. Stromquist, Packing layered posets into posets, manuscript.
%H A061061 Miklos Bona, Bruce E. Sagan and Vincent R. Vatter, <a href="http://arXiv.org/abs/math.CO/0104098">Pattern frequency sequences and internal zeros</a>
%H A061061 Alejandro H. Morales, Igor Pak, Greta Panova, <a href="https://arxiv.org/abs/1805.04341">Asymptotics of principal evaluations of Schubert polynomials for layered permutations</a>, arXiv:1805.04341 [math.CO], 2018.
%F A061061 a(n) = max(a(k) + k*C(n-k, 2): 1 <= k < n)
%F A061061 a(n+1)/a(n)=1+3/n+O(1/n^2). n^2*(a(n+1)/a(n)-1-3/n) is bounded but there is no limit; limit n-->infinity a(n)/n^3 = C = 0.0773... - _Benoit Cloitre_, Jan 25 2003
%e A061061 a(8) = 31; the permutation of 1..8 containing the maximum number of 132 patterns is 13287654.
%K A061061 easy,nonn
%O A061061 1,4
%A A061061 _Michael Albert_, May 27 2001
%E A061061 More terms from _Vladeta Jovovic_, Jun 03 2001