%I #13 Jul 18 2020 10:05:17

%S 0,0,8,483,16205,430078,10210206,228926441,4979392831,106552681812,

%T 2260112122016,47713890438655,1004771692065345,21130651257100970,

%U 444074589574292578,9329140064903065365,195950323696361689667,4115367075816142112512,86427075922333935342372

%N 1/3 of the number of permutations of 2 indistinguishable copies of 1..n with exactly 3 local maxima.

%H Andrew Howroyd, <a href="/A152495/b152495.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 (50,-916,7914,-34047,70740,-56700).

%F a(n) = A334774(n,3)/3. - _Andrew Howroyd_, May 12 2020

%F From _Colin Barker_, Jul 18 2020: (Start)

%F G.f.: x^3*(8 + 83*x - 617*x^2 - 1056*x^3) / ((1 - 3*x)^3*(1 - 10*x)^2*(1 - 21*x)).

%F a(n) = 50*a(n-1) - 916*a(n-2) + 7914*a(n-3) - 34047*a(n-4) + 70740*a(n-5) - 56700*a(n-6) for n>6.

%F (End)

%o (PARI) \\ PeaksBySig defined in A334774.

%o a(n) = {PeaksBySig(vector(n,i,2), [2])[1]/3} \\ _Andrew Howroyd_, May 12 2020

%o (PARI) concat([0,0], Vec(x^3*(8 + 83*x - 617*x^2 - 1056*x^3) / ((1 - 3*x)^3*(1 - 10*x)^2*(1 - 21*x)) + O(x^22))) \\ _Colin Barker_, Jul 18 2020

%Y Cf. A334774.

%K nonn,easy

%O 1,3

%A _R. H. Hardin_, Dec 06 2008

%E Terms a(12) and beyond from _Andrew Howroyd_, May 11 2020