login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

1/3 of the number of permutations of 2 indistinguishable copies of 1..n with exactly 2 local maxima.
9

%I #12 May 19 2020 15:10:51

%S 0,1,19,235,2539,26119,263863,2648107,26513875,265250287,2652876847,

%T 26530008499,265304159371,2653054879735,26530591844071,

%U 265306057146811,2653061016284227,26530611583384063,265306120353746335,2653061217872021443,26530612224048411643

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

%H Andrew Howroyd, <a href="/A152494/b152494.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (16,-69,90).

%F a(n) = (13*10^(n-1) - 13*3^(n-1) - 14*(n-1)*3^(n-1))/49. - _Andrew Howroyd_, May 10 2020

%F From _Colin Barker_, May 19 2020: (Start)

%F G.f.: x*(1 + 3*x) / ((1 - 3*x)^2*(1 - 10*x)).

%F a(n) = 16*a(n-1) - 69*a(n-2) + 90*a(n-3) for n>3.

%F (End)

%o (PARI) a(n) = {(13*10^(n-1) - 13*3^(n-1) - 14*(n-1)*3^(n-1))/49} \\ _Andrew Howroyd_, May 10 2020

%o (PARI) concat(0, Vec(x*(1 + 3*x) / ((1 - 3*x)^2*(1 - 10*x)) + O(x^20))) \\ _Colin Barker_, May 19 2020

%Y Cf. A334773.

%K nonn,easy

%O 1,3

%A _R. H. Hardin_, Dec 06 2008

%E Terms a(12) and beyond from _Andrew Howroyd_, May 10 2020