A152494 1/3 of the number of permutations of 2 indistinguishable copies of 1..n with exactly 2 local maxima.
0, 1, 19, 235, 2539, 26119, 263863, 2648107, 26513875, 265250287, 2652876847, 26530008499, 265304159371, 2653054879735, 26530591844071, 265306057146811, 2653061016284227, 26530611583384063, 265306120353746335, 2653061217872021443, 26530612224048411643
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (16,-69,90).
Crossrefs
Cf. A334773.
Programs
-
PARI
a(n) = {(13*10^(n-1) - 13*3^(n-1) - 14*(n-1)*3^(n-1))/49} \\ Andrew Howroyd, May 10 2020 -
PARI
concat(0, Vec(x*(1 + 3*x) / ((1 - 3*x)^2*(1 - 10*x)) + O(x^20))) \\ Colin Barker, May 19 2020
Formula
a(n) = (13*10^(n-1) - 13*3^(n-1) - 14*(n-1)*3^(n-1))/49. - Andrew Howroyd, May 10 2020
From Colin Barker, May 19 2020: (Start)
G.f.: x*(1 + 3*x) / ((1 - 3*x)^2*(1 - 10*x)).
a(n) = 16*a(n-1) - 69*a(n-2) + 90*a(n-3) for n>3.
(End)
Extensions
Terms a(12) and beyond from Andrew Howroyd, May 10 2020