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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 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.)