A152514 1/7 of the number of permutations of 6 indistinguishable copies of 1..n with exactly 3 local maxima.
0, 50, 42035, 22286180, 10637332433, 4951385566862, 2291336707020095, 1058974724436063848, 489282897651319234589, 226052182024142033107730, 104436435218150212780973867, 48249663449218668484434011660, 22291347308935948403947280066153, 10298602712004866151067473095589974
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (651,-98049,5130937,-81120186,508243680,-1118136096).
Programs
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PARI
\\ PeaksBySig defined in A334774. a(n) = {PeaksBySig(vector(n,i,6), [2])[1]/7} \\ Andrew Howroyd, May 12 2020
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PARI
concat(0, Vec(x^2*(50 + 9485*x - 176155*x^2 - 6027882*x^3 - 3111696*x^4) / ((1 - 7*x)^3*(1 - 84*x)^2*(1 - 462*x)) + O(x^15))) \\ Colin Barker, Jul 19 2020
Formula
From Colin Barker, Jul 19 2020: (Start)
G.f.: x^2*(50 + 9485*x - 176155*x^2 - 6027882*x^3 - 3111696*x^4) / ((1 - 7*x)^3*(1 - 84*x)^2*(1 - 462*x)).
a(n) = 651*a(n-1) - 98049*a(n-2) + 5130937*a(n-3) - 81120186*a(n-4) + 0*a(n-5) - 0*a(n-6) for n>6.
(End)
Extensions
Terms a(7) and beyond from Andrew Howroyd, May 12 2020