A151590 Number of permutations of 3 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.

0, 12, 207, 1392, 7455, 36540, 171591, 785856, 3538215, 15727740, 69204927, 301988592, 1308621327, 5637142812, 24159189015, 103079212800, 438086661591, 1855425868956, 7834020344655, 32985348829680, 138538465095807, 580542139461372, 2427721674124647

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (11,-43,73,-56,16).

Formula

a(n) = n*((3/2)*4^n - 9*n) for n > 1. - Andrew Howroyd, May 04 2020

From Colin Barker, Jul 16 2020: (Start)

G.f.: 3*x^2*(4 + 25*x - 123*x^2 + 56*x^3 - 16*x^4) / ((1 - x)^3*(1 - 4*x)^2).

a(n) = 11*a(n-1) - 43*a(n-2) + 73*a(n-3) - 56*a(n-4) + 16*a(n-5) for n>6.

(End)

Prog

(PARI) a(n) = if(n <= 1, 0, n*(3*4^n/2 - 9*n)) \\ Andrew Howroyd, May 04 2020
(PARI) concat(0, Vec(3*x^2*(4 + 25*x - 123*x^2 + 56*x^3 - 16*x^4) / ((1 - x)^3*(1 - 4*x)^2) + O(x^40))) \\ Colin Barker, Jul 16 2020

Crossrefs

Cf. A151583.

Sequence in context: A051688 A198529 A372616 * A297311 A217703 A245911

Adjacent sequences: A151587 A151588 A151589 * A151591 A151592 A151593

Keyword

nonn,easy

Author

R. H. Hardin, May 21 2009

Extensions

Terms a(9) and beyond from Andrew Howroyd, May 04 2020

Status

approved