A152500 1/4 the number of permutations of 3 indistinguishable copies of 1..n with exactly 3 local maxima.
0, 1, 231, 21490, 1476084, 90050080, 5228286336, 297239712256, 16749407726592, 940343619493888, 52712719000338432, 2953100593082269696, 165399775808105742336, 9262957817232621568000, 518737995604927325405184, 29049593918675470746910720, 1626782962901824260072800256
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (108,-3840,58752,-401664,1244160,-1433600).
Programs
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PARI
\\ PeaksBySig defined in A334774. a(n) = {PeaksBySig(vector(n,i,3), [2])[1]/4} \\ Andrew Howroyd, May 12 2020
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PARI
concat(0, Vec(x^2*(1 + 123*x + 382*x^2 - 16548*x^3 - 15440*x^4) / ((1 - 4*x)^3*(1 - 20*x)^2*(1 - 56*x)) + O(x^19))) \\ Colin Barker, Jul 19 2020
Formula
From Colin Barker, Jul 19 2020: (Start)
G.f.: x^2*(1 + 123*x + 382*x^2 - 16548*x^3 - 15440*x^4) / ((1 - 4*x)^3*(1 - 20*x)^2*(1 - 56*x)).
a(n) = 108*a(n-1) - 3840*a(n-2) + 58752*a(n-3) - 401664*a(n-4) + 1244160*a(n-5) - 1433600*a(n-6) for n>6.
(End)
Extensions
Terms a(10) and beyond from Andrew Howroyd, May 12 2020