A159737 Number of permutations of 6 indistinguishable copies of 1..n arranged in a circle with exactly 2 local maxima.
150, 22680, 2596608, 273322980, 27558217008, 2700777267972, 259275295383552, 24501521550788100, 2286808732032093360, 211301127303186249252, 19362866942233277773632, 1762020891775616889450852, 159395120671659354639719856, 14345560860451487040265198020
Offset: 2
Links
- Andrew Howroyd, Table of n, a(n) for n = 2..200
- Index entries for linear recurrences with constant coefficients, signature (189,-10731,173215,-1094856,2420208).
Programs
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PARI
a(n) = {3*n*(61^2*84^(n-2) + 96*7^(n-2) - 396*n*7^(n-2))/121} \\ Andrew Howroyd, May 10 2020 -
PARI
Vec(6*x^2*(5 + 7*x)*(5 - 196*x - 2401*x^2 + 2058*x^3) / ((1 - 7*x)^3*(1 - 84*x)^2) + O(x^40)) \\ Colin Barker, Jul 18 2020
Formula
a(n) = 3*n*(61^2*84^(n-2) + 96*7^(n-2) - 396*n*7^(n-2))/121. - Andrew Howroyd, May 10 2020
From Colin Barker, Jul 18 2020: (Start)
G.f.: 6*x^2*(5 + 7*x)*(5 - 196*x - 2401*x^2 + 2058*x^3) / ((1 - 7*x)^3*(1 - 84*x)^2).
a(n) = 189*a(n-1) - 10731*a(n-2) + 173215*a(n-3) - 1094856*a(n-4) + 2420208*a(n-5) for n>6.
(End)
Extensions
Terms a(7) and beyond from Andrew Howroyd, May 09 2020