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

1,2

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).

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)

Prog

(PARI) \\ PeaksBySig defined in A334774.
a(n) = {PeaksBySig(vector(n, i, 4), [2])[1]/10} \\ Andrew Howroyd, May 12 2020
(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

Crossrefs

Cf. A152504, A334774.

Sequence in context: A358269 A167069 A024046 * A139301 A004803 A065604

Adjacent sequences: A152502 A152503 A152504 * A152506 A152507 A152508

Keyword

nonn,easy

Author

R. H. Hardin, Dec 06 2008

Extensions

Terms a(8) and beyond from Andrew Howroyd, May 12 2020

Status

approved