A300781 Number of log-concave permutations of {1,...,n}.

1, 1, 2, 4, 8, 10, 14, 18, 22, 18, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12

Offset

0,3

Comments

a(n) = 12 for n >= 10, since for these n the only log-concave permutations of {1,...,n} are (1,2,...,n), (1,2,4,5,...,n,3), (1,2,4,6,...,7,5,3), (1,3,4,...,n,2), (1,3,5,...,6,4,2), (1,n,...,3,2), and the reverses of these.

Links

Table of n, a(n) for n=0..78.

Pontus Andersson (von Brömssen), Log-concave permutations, Manuscript, 2002.

Eric Weisstein's World of Mathematics, Logarithmically Concave Sequence.

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

G.f.: (6*x^10 +4*x^9 -4*x^8 -4*x^7 -4*x^6 -2*x^5 -4*x^4 -2*x^3 -x^2 -1)/(x-1).

Crossrefs

Cf. A069916, A301454.

Sequence in context: A341822 A363797 A034822 * A050567 A069879 A074330

Adjacent sequences: A300778 A300779 A300780 * A300782 A300783 A300784

Keyword

easy,nonn

Author

Pontus von Brömssen, Mar 12 2018

Status

approved