A159721 Number of permutations of 3 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
6, 36, 192, 960, 4608, 21504, 98304, 442368, 1966080, 8650752, 37748736, 163577856, 704643072, 3019898880, 12884901888, 54760833024, 231928233984, 979252543488, 4123168604160, 17317308137472, 72567767433216, 303465209266176, 1266637395197952, 5277655813324800
Offset: 2
Links
- R. H. Hardin, Table of n, a(n) for n = 2..100
- Index entries for linear recurrences with constant coefficients, signature (8,-16).
Programs
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Magma
[3*n*4^(n-2): n in [2..30]]; // G. C. Greubel, Jun 01 2018
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Mathematica
LinearRecurrence[{8,-16}, {6,36}, 30] (* or *) Table[3*n*4^(n-2), {n, 2, 30}] (* G. C. Greubel, Jun 01 2018 *) -
PARI
for(n=2,30, print1(3*n*4^(n-2), ", ")) \\ G. C. Greubel, Jun 01 2018
Formula
a(n) = (copies*n)*(copies+1)^(n-2), here: copies = 3.
From Colin Barker, Mar 23 2018: (Start)
G.f.: 6*x^2*(1 - 2*x) / (1 - 4*x)^2.
a(n) = 8*a(n-1) - 16*a(n-2) for n>3. (End)
E.g.f.: 3*x*exp(4*x)/4. - G. C. Greubel, Jun 01 2018
From Amiram Eldar, May 16 2022: (Start)
Sum_{n>=2} 1/a(n) = (16/3)*log(4/3) - 3/2.
Sum_{n>=2} (-1)^n/a(n) = (16/3)*log(5/4) - 7/6. (End)