A152495 1/3 of the number of permutations of 2 indistinguishable copies of 1..n with exactly 3 local maxima.

0, 0, 8, 483, 16205, 430078, 10210206, 228926441, 4979392831, 106552681812, 2260112122016, 47713890438655, 1004771692065345, 21130651257100970, 444074589574292578, 9329140064903065365, 195950323696361689667, 4115367075816142112512, 86427075922333935342372

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 (50,-916,7914,-34047,70740,-56700).

Crossrefs

Cf. A334774.

Programs

PARI

\\ PeaksBySig defined in A334774.
a(n) = {PeaksBySig(vector(n,i,2), [2])[1]/3} \\ Andrew Howroyd, May 12 2020

PARI

concat([0,0], Vec(x^3*(8 + 83*x - 617*x^2 - 1056*x^3) / ((1 - 3*x)^3*(1 - 10*x)^2*(1 - 21*x)) + O(x^22))) \\ Colin Barker, Jul 18 2020

Formula

a(n) = A334774(n,3)/3. - Andrew Howroyd, May 12 2020

From Colin Barker, Jul 18 2020: (Start)

G.f.: x^3*(8 + 83*x - 617*x^2 - 1056*x^3) / ((1 - 3*x)^3*(1 - 10*x)^2*(1 - 21*x)).

a(n) = 50*a(n-1) - 916*a(n-2) + 7914*a(n-3) - 34047*a(n-4) + 70740*a(n-5) - 56700*a(n-6) for n>6.

(End)

Extensions

Terms a(12) and beyond from Andrew Howroyd, May 11 2020