A159715 Number of permutations of 2 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.

4, 18, 72, 270, 972, 3402, 11664, 39366, 131220, 433026, 1417176, 4605822, 14880348, 47829690, 153055008, 487862838, 1549681956, 4907326194, 15496819560, 48814981614, 153418513644, 481176247338, 1506290861232, 4707158941350

Offset

2,1

Links

R. H. Hardin, Table of n, a(n) for n = 2..100

Index entries for linear recurrences with constant coefficients, signature (6,-9).

Formula

a(n) = (copies*n)*(copies+1)^(n-2), here: copies = 2.

Apparently a(n) = A027261(n-1), n > 2. - R. J. Mathar, Apr 21 2009

Conjectures from Colin Barker, Mar 23 2018: (Start)

G.f.: 2*x^2*(2 - 3*x) / (1 - 3*x)^2.

a(n) = 2*3^(n-2)*n for n>1.

a(n) = 6*a(n-1) - 9*a(n-2) for n>3. (End)

E.g.f.: 2*x*exp(3*x)/3. - G. C. Greubel, Jun 01 2018

From Amiram Eldar, May 16 2022: (Start)

Sum_{n>=2} 1/a(n) = (9/2)*log(3/2) - 3/2.

Sum_{n>=2} (-1)^n/a(n) = 3/2 - (9/2)*log(4/3). (End)

Mathematica

LinearRecurrence[{6, -9}, {}, 30] (* or *) Table[2*n*3^(n-2), {n, 2, 30}] (* G. C. Greubel, Jun 01 2018 *)

Prog

(PARI) for(n=2, 30, print1(2*n*3^(n-2), ", ")) \\ G. C. Greubel, Jun 01 2018
(Magma) [2*n*3^(n-2): n in [2..30]]; // G. C. Greubel, Jun 01 2018

Crossrefs

Cf. A027261, A159721, A159727, A159733, A159736, A159738, A159739, A159740.

Sequence in context: A263582 A034352 A358463 * A027261 A290919 A218892

Adjacent sequences: A159712 A159713 A159714 * A159716 A159717 A159718

Keyword

nonn

Author

R. H. Hardin, Apr 20 2009

Status

approved