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

1,3

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).

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)

Prog

(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

Crossrefs

Cf. A334774.

Sequence in context: A203526 A210117 A204564 * A197096 A332148 A109060

Adjacent sequences: A152492 A152493 A152494 * A152496 A152497 A152498

Keyword

nonn,easy

Author

R. H. Hardin, Dec 06 2008

Extensions

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

Status

approved