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A301454 Number of strictly log-concave permutations of {1,...,n}.

%I A301454 #21 Feb 16 2025 08:33:53
%S A301454 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,
%T A301454 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,
%U A301454 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
%N A301454 Number of strictly log-concave permutations of {1,...,n}.
%C A301454 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.
%H A301454 Pontus Andersson (von Brömssen), <a href="/A301454/a301454.pdf">Log-concave permutations</a>, Manuscript, 2002.
%H A301454 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LogarithmicallyConcaveSequence.html">Logarithmically Concave Sequence</a>
%H A301454 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A301454 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).
%t A301454 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 *)
%o A301454 (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
%Y A301454 Cf. A300781.
%K A301454 easy,nonn
%O A301454 0,3
%A A301454 _Pontus von Brömssen_, Mar 21 2018