A159711 Number of permutations of 1..n arranged in a circle with exactly 3 local maxima.

0, 0, 0, 0, 0, 0, 96, 1904, 23040, 221184, 1858560, 14353152, 104742912, 734769152, 5010432000, 33464217600, 220066480128, 1430279159808, 9212045819904, 58914039332864, 374665295953920, 2371935399837696, 14960708435312640, 94072038170296320, 589975504803594240

Offset: 0

Author

R. H. Hardin, Apr 20 2009

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (32,-444,3504,-17328,55680,-116288,152320,-113664,36864).

Crossrefs

Column k=3 of A263789.

Programs

Magma

[(1/3)*2^(-6+n)*n*(15+3*2^(1+n)+3^n-3*(8+2^n)*n+6*n^2): n in [0..30]]; // G. C. Greubel, Jun 01 2018

Mathematica

Table[(1/3)*2^(-6+n)*n*(15+3*2^(1+n)+3^n-3*(8+2^n)*n+6*n^2), {n,0,30}] (* G. C. Greubel, Jun 01 2018 *)

PARI

a(n) = if(n==1, 0, 1/3*2^(-6+n)*n*(15+3*2^(1+n)+3^n-3*(8+2^n)*n +6*n^2)) \\ Colin Barker, Oct 26 2015

PARI

concat(vector(6), Vec(-16*x^6*(144*x^4-444*x^3+296*x^2-73*x+6)/(
(2*x-1)^4*(4*x-1)^3*(6*x-1)^2) + O(x^30))) \\ Colin Barker, Oct 26 2015

Formula

G.f.: -16*(144*x^4-444*x^3+296*x^2-73*x+6)*x^6 / ((6*x-1)^2 *(4*x-1)^3 *(2*x-1)^4). - Alois P. Heinz, Oct 26 2015

a(n) = 1/3*2^(-6+n)*n*(15+3*2^(1+n)+3^n-3*(8+2^n)*n+6*n^2) for n>1. - Colin Barker, Oct 26 2015

Extensions

a(17)-a(24) from Alois P. Heinz, Oct 26 2015