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A151583
Number of permutations of 2 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
6
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
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.
Sequence in context: A317432 A302468 A303250 * A325935 A360065 A222997
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, May 21 2009
EXTENSIONS
Terms a(13) and beyond from Andrew Howroyd, May 04 2020
STATUS
approved