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%I #9 Jul 19 2020 07:21:50
%S 0,1,231,21490,1476084,90050080,5228286336,297239712256,
%T 16749407726592,940343619493888,52712719000338432,2953100593082269696,
%U 165399775808105742336,9262957817232621568000,518737995604927325405184,29049593918675470746910720,1626782962901824260072800256
%N 1/4 the number of permutations of 3 indistinguishable copies of 1..n with exactly 3 local maxima.
%H Andrew Howroyd, <a href="/A152500/b152500.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (108,-3840,58752,-401664,1244160,-1433600).
%F From _Colin Barker_, Jul 19 2020: (Start)
%F G.f.: x^2*(1 + 123*x + 382*x^2 - 16548*x^3 - 15440*x^4) / ((1 - 4*x)^3*(1 - 20*x)^2*(1 - 56*x)).
%F a(n) = 108*a(n-1) - 3840*a(n-2) + 58752*a(n-3) - 401664*a(n-4) + 1244160*a(n-5) - 1433600*a(n-6) for n>6.
%F (End)
%o (PARI) \\ PeaksBySig defined in A334774.
%o a(n) = {PeaksBySig(vector(n,i,3), [2])[1]/4} \\ _Andrew Howroyd_, May 12 2020
%o (PARI) concat(0, Vec(x^2*(1 + 123*x + 382*x^2 - 16548*x^3 - 15440*x^4) / ((1 - 4*x)^3*(1 - 20*x)^2*(1 - 56*x)) + O(x^19))) \\ _Colin Barker_, Jul 19 2020
%Y Cf. A152499, A334774.
%K nonn,easy
%O 1,3
%A _R. H. Hardin_, Dec 06 2008
%E Terms a(10) and beyond from _Andrew Howroyd_, May 12 2020