A159739 Number of permutations of 8 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
16, 216, 2592, 29160, 314928, 3306744, 34012224, 344373768, 3443737680, 34093003032, 334731302496, 3263630199336, 31632108085872, 305023899399480, 2928229434235008, 28001193964872264, 266834907194665104, 2534931618349318488, 24015141647519859360
Offset: 2
Links
- R. H. Hardin, Table of n, a(n) for n=2..100
- Index entries for linear recurrences with constant coefficients, signature (18,-81).
Programs
-
Magma
I:=[16, 216]; [n le 2 select I[n] else 18*Self(n-1) - 81*Self(n-2): n in [1..30]]; // G. C. Greubel, Jun 01 2018
-
Mathematica
LinearRecurrence[{18,-81}, {16,216}, 30] (* G. C. Greubel, Jun 01 2018 *) -
PARI
Vec(8*x^2*(2 - 9*x) / (1 - 9*x)^2 + O(x^25)) \\ Colin Barker, Feb 26 2018
Formula
a(n) = (copies*n)*(copies+1)^(n-2) with copies = 8.
a(n) = 8*n*9^(n-2).
From Colin Barker, Feb 26 2018: (Start)
G.f.: 8*x^2*(2 - 9*x) / (1 - 9*x)^2.
a(n) = 18*a(n-1) - 81*a(n-2) for n>3.
(End)
From Amiram Eldar, May 16 2022: (Start)
Sum_{n>=2} 1/a(n) = (81/8)*log(9/8) - 9/8.
Sum_{n>=2} (-1)^n/a(n) = 9/8 - (81/8)*log(10/9). (End)