A159716 Number of permutations of 2 indistinguishable copies of 1..n arranged in a circle with exactly 2 local maxima.

2, 66, 1168, 16220, 202416, 2395540, 27517568, 310123764, 3447919120, 37934904788, 413863668480, 4483624403284, 48285543009872, 517346347249140, 5518365322864384, 58632646191319220, 620816303380261392, 6553061146974071956, 68979591578665208960, 724285713430953995412

Offset: 2

Author

R. H. Hardin, Apr 20 2009

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..200
• Index entries for linear recurrences with constant coefficients, signature (29,-307,1467,-3240,2700).

Crossrefs

Column k=2 of A334772.

Programs

PARI

a(n) = {n*(169*10^(n-2) + 48*3^(n-2) - 84*n*3^(n-2))/49} \\ Andrew Howroyd, May 10 2020

PARI

Vec(2*x*(1 + 3*x)*(1 + x - 69*x^2 + 45*x^3) / ((1 - 3*x)^3*(1 - 10*x)^2) + O(x^20)) \\ Colin Barker, May 19 2020

Formula

a(n) = n*(169*10^(n-2) + 48*3^(n-2) - 84*n*3^(n-2))/49. - Andrew Howroyd, May 10 2020

From Colin Barker, May 19 2020: (Start)

G.f.: 2*x*(1 + 3*x)*(1 + x - 69*x^2 + 45*x^3) / ((1 - 3*x)^3*(1 - 10*x)^2).

a(n) = 29*a(n-1) - 307*a(n-2) + 1467*a(n-3) - 3240*a(n-4) + 2700*a(n-5) for n>6.

(End)

Extensions

Terms a(11) and beyond from Andrew Howroyd, May 09 2020