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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
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
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).
MATHEMATICA
CoefficientList[Series[(4*x^9 - 2*x^7 - 2*x^6 - 2*x^5 - 2*x^4 - 2*x^3 - x^2 - 1)/(x - 1), {x, 0, 100}], x] (* Wesley Ivan Hurt, Dec 26 2023 *)
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: A366021 A365453 A365984 * A161602 A359496 A356066
KEYWORD
easy,nonn
AUTHOR
STATUS
approved