A152510 1/60 of the number of permutations of 5 indistinguishable copies of 1..n with exactly 3 local maxima.

0, 2, 1066, 328314, 87554515, 22414176982, 5672480870616, 1431066048773744, 360732335571459920, 90911141639422741152, 22910020941551289849856, 5773350885207751422091264, 1454885995214232796339050240, 366631366567387199476086758912, 92391110171365499708617443239936

Offset: 1

Author

R. H. Hardin, Dec 06 2008

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (382,-38020,1394280,-17690400,92123136,-170698752).

Crossrefs

Cf. A152509, A334774.

Programs

Mathematica

LinearRecurrence[{382,-38020,1394280,-17690400,92123136,-170698752},{0,2,1066,328314,87554515,22414176982},20] (* Harvey P. Dale, Mar 14 2022 *)

PARI

\\ PeaksBySig defined in A334774.
a(n) = {PeaksBySig(vector(n,i,5), [2])[1]/60} \\ Andrew Howroyd, May 12 2020

PARI

concat(0, Vec(x^2*(2 + 302*x - 2858*x^2 - 120673*x^3 - 71148*x^4) / ((1 - 6*x)^3*(1 - 56*x)^2*(1 - 252*x)) + O(x^20))) \\ Colin Barker, Jul 19 2020

Formula

From Colin Barker, Jul 19 2020: (Start)

G.f.: x^2*(2 + 302*x - 2858*x^2 - 120673*x^3 - 71148*x^4) / ((1 - 6*x)^3*(1 - 56*x)^2*(1 - 252*x)).

a(n) = 382*a(n-1) - 38020*a(n-2) + 1394280*a(n-3) - 17690400*a(n-4) + 92123136*a(n-5) - 170698752*a(n-6) for n>6.

(End)

Extensions

Terms a(7) and beyond from Andrew Howroyd, May 12 2020