A152505 1/10 of the number of permutations of 4 indistinguishable copies of 1..n with exactly 3 local maxima.
0, 3, 1008, 172573, 24118698, 3148308323, 401420959948, 50776368194073, 6405835208453198, 807454401764399823, 101751780468757346448, 12821210170324927605573, 1615491145485759589239698, 203552595669637872843811323, 25647653984634161426074132948
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (211,-13060,319850,-3093125,12831875,-19293750).
Programs
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PARI
\\ PeaksBySig defined in A334774. a(n) = {PeaksBySig(vector(n,i,4), [2])[1]/10} \\ Andrew Howroyd, May 12 2020
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PARI
concat(0, Vec(x^2*(3 + 375*x - 935*x^2 - 89275*x^3 - 63000*x^4) / ((1 - 5*x)^3*(1 - 35*x)^2*(1 - 126*x)) + O(x^15))) \\ Colin Barker, Jul 19 2020
Formula
From Colin Barker, Jul 19 2020: (Start)
G.f.: x^2*(3 + 375*x - 935*x^2 - 89275*x^3 - 63000*x^4) / ((1 - 5*x)^3*(1 - 35*x)^2*(1 - 126*x)).
a(n) = 211*a(n-1) - 13060*a(n-2) + 319850*a(n-3) - 3093125*a(n-4) + 12831875*a(n-5) - 19293750*a(n-6) for n>6.
(End)
Extensions
Terms a(8) and beyond from Andrew Howroyd, May 12 2020