A159722 Number of permutations of 3 indistinguishable copies of 1..n arranged in a circle with exactly 2 local maxima.
12, 576, 17376, 448800, 10861056, 253940736, 5807161344, 130675728384, 2903978803200, 63887897001984, 1393919508086784, 30201597684350976, 650495989232173056, 13939199950454784000, 297369599774111563776, 6319103998978368208896, 133816319995412169621504
Offset: 2
Links
- Andrew Howroyd, Table of n, a(n) for n = 2..200
- Index entries for linear recurrences with constant coefficients, signature (52,-928,6784,-21760,25600).
Programs
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PARI
a(n) = {3*n*(121*20^(n-2) + 15*4^(n-2) - 36*n*4^(n-2))/32} \\ Andrew Howroyd, May 10 2020 -
PARI
Vec(12*x*(1 + 2*x)*(1 - 6*x - 108*x^2 + 80*x^3) / ((1 - 4*x)^3*(1 - 20*x)^2) + O(x^20)) \\ Colin Barker, Jul 16 2020
Formula
a(n) = 3*n*(121*20^(n-2) + 15*4^(n-2) - 36*n*4^(n-2))/32. - Andrew Howroyd, May 10 2020
From Colin Barker, Jul 16 2020: (Start)
G.f.: 12*x*(1 + 2*x)*(1 - 6*x - 108*x^2 + 80*x^3) / ((1 - 4*x)^3*(1 - 20*x)^2).
a(n) = 52*a(n-1) - 928*a(n-2) + 6784*a(n-3) - 21760*a(n-4) + 25600*a(n-5) for n>6.
(End)
Extensions
Terms a(9) and beyond from Andrew Howroyd, May 09 2020