A152499 1/12 of the number of permutations of 3 indistinguishable copies of 1..n with exactly 2 local maxima.
0, 1, 30, 664, 13632, 274432, 5497344, 109987840, 2199945216, 43999756288, 879998926848, 17599995314176, 351999979683840, 7039999912443904, 140799999624609792, 2815999998397775872, 56319999993188450304, 1126399999971143188480, 22527999999878130302976
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (28,-176,320).
Programs
-
PARI
a(n) = {(11*20^(n-1) - 11*4^(n-1) - 12*(n-1)*4^(n-1))/128} \\ Andrew Howroyd, May 10 2020 -
PARI
concat(0, Vec(x^2*(1 + 2*x) / ((1 - 4*x)^2*(1 - 20*x)) + O(x^40))) \\ Colin Barker, Jul 15 2020
Formula
a(n) = (11*20^(n-1) - 11*4^(n-1) - 12*(n-1)*4^(n-1))/128. - Andrew Howroyd, May 10 2020
From Colin Barker, Jul 15 2020: (Start)
G.f.: x^2*(1 + 2*x) / ((1 - 4*x)^2*(1 - 20*x)).
a(n) = 28*a(n-1) - 176*a(n-2) + 320*a(n-3) for n>2.
(End)
Extensions
Terms a(10) and beyond from Andrew Howroyd, May 10 2020