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

2,1

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).

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)

Prog

(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

Crossrefs

Column k=2 of A334772.

Sequence in context: A226338 A131472 A098532 * A157060 A154637 A069865

Adjacent sequences: A159713 A159714 A159715 * A159717 A159718 A159719

Keyword

nonn,easy

Author

R. H. Hardin, Apr 20 2009

Extensions

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

Status

approved