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

Author

R. H. Hardin, May 21 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A151583.

Programs

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

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)

Extensions

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