OFFSET
1,4
COMMENTS
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
REFERENCES
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.
W. Stromquist, Packing layered posets into posets, manuscript.
LINKS
Miklos Bona, Bruce E. Sagan and Vincent R. Vatter, Pattern frequency sequences and internal zeros
Alejandro H. Morales, Igor Pak, Greta Panova, Asymptotics of principal evaluations of Schubert polynomials for layered permutations, arXiv:1805.04341 [math.CO], 2018.
FORMULA
a(n) = max(a(k) + k*C(n-k, 2): 1 <= k < n)
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
EXAMPLE
a(8) = 31; the permutation of 1..8 containing the maximum number of 132 patterns is 13287654.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Michael Albert, May 27 2001
EXTENSIONS
More terms from Vladeta Jovovic, Jun 03 2001
STATUS
approved