A152504 1/10 of the number of permutations of 4 indistinguishable copies of 1..n with exactly 2 local maxima.
0, 3, 140, 5175, 183000, 6416875, 224662500, 7863609375, 275228750000, 9633019921875, 337155773437500, 11800452490234375, 413015839453125000, 14455554393310546875, 505944403833007812500, 17708054134515380859375, 619781894709960937500000, 21692366314858856201171875
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (45,-375,875).
Programs
-
PARI
a(n) = {(11*35^(n-1) - 11*5^(n-1) - 12*(n-1)*5^(n-1))/90} \\ Andrew Howroyd, May 10 2020 -
PARI
concat(0, Vec(x^2*(3 + 5*x) / ((1 - 5*x)^2*(1 - 35*x)) + O(x^20))) \\ Colin Barker, Jul 16 2020
Formula
a(n) = (11*35^(n-1) - 11*5^(n-1) - 12*(n-1)*5^(n-1))/90. - Andrew Howroyd, May 10 2020
From Colin Barker, Jul 16 2020: (Start)
G.f.: x^2*(3 + 5*x) / ((1 - 5*x)^2*(1 - 35*x)).
a(n) = 45*a(n-1) - 375*a(n-2) + 875*a(n-3) for n>3.
(End)
Extensions
Terms a(9) and beyond from Andrew Howroyd, May 10 2020