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
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).
Crossrefs
Programs
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PARI
a(n) = if(n <= 1, 0, n*(3^n - 4*n)) \\ Andrew Howroyd, May 04 2020
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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
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)
Extensions
Terms a(13) and beyond from Andrew Howroyd, May 04 2020