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A301454 Number of strictly log-concave permutations of {1,...,n}. 2
1, 1, 2, 4, 6, 8, 10, 12, 12, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = 8 for n >= 9, since for these n the only strictly log-concave permutations of {1,...,n} are (1,2,...,n), (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..105.

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

Eric Weisstein's World of Mathematics, Logarithmically Concave Sequence

FORMULA

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

PROG

(PARI) Vec((4*x^9 -2*x^7 -2*x^6 -2*x^5 -2*x^4 -2*x^3 -x^2 -1)/(x-1) + O(x^100)) \\ Felix Fröhlich, Mar 23 2018

CROSSREFS

Cf. A300781.

Sequence in context: A241071 A319807 A055954 * A161602 A285591 A327210

Adjacent sequences:  A301451 A301452 A301453 * A301455 A301456 A301457

KEYWORD

easy,nonn

AUTHOR

Pontus von Brömssen, Mar 21 2018

STATUS

approved

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Last modified January 28 06:29 EST 2020. Contains 331317 sequences. (Running on oeis4.)