A151583 Number of permutations of 2 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.

0, 2, 45, 260, 1115, 4230, 15113, 52232, 176823, 590090, 1948133, 6376716, 20725523, 66960782, 215232705, 688746512, 2195381615, 6973567506, 22082966429, 69735686420, 219667415499, 690383309462, 2165293110905, 6778308873240, 21182215233575, 66088511533850

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (9,-30,46,-33,9).

Formula

a(n) = n*(3^n - 4*n) for n > 1. - Andrew Howroyd, May 04 2020

From Colin Barker, Jul 15 2020: (Start)

G.f.: x^2*(2 + 27*x - 85*x^2 + 33*x^3 - 9*x^4) / ((1 - x)^3*(1 - 3*x)^2).

a(n) = 9*a(n-1) - 30*a(n-2) + 46*a(n-3) - 33*a(n-4) + 9*a(n-5) for n>6.

(End)

Prog

(PARI) a(n) = if(n <= 1, 0, n*(3^n - 4*n)) \\ Andrew Howroyd, May 04 2020
(PARI) concat(0, Vec(x^2*(2 + 27*x - 85*x^2 + 33*x^3 - 9*x^4) / ((1 - x)^3*(1 - 3*x)^2) + O(x^30))) \\ Colin Barker, Jul 15 2020

Crossrefs

With 3..8 descents: A151584, A151585, A151586, A151587, A151588, A151589.

With 3..7 copies of 1..n: A151590, A151597, A151603, A151607, A151610.

Cf. A151576, A151624.

Sequence in context: A317432 A302468 A303250 * A325935 A360065 A222997

Adjacent sequences: A151580 A151581 A151582 * A151584 A151585 A151586

Keyword

nonn,easy

Author

R. H. Hardin, May 21 2009

Extensions

Terms a(13) and beyond from Andrew Howroyd, May 04 2020

Status

approved