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A151576
Number of permutations of 1..n arranged in a circle with exactly 3 adjacent element pairs in decreasing order.
3
0, 4, 55, 396, 2114, 9528, 38637, 146080, 526240, 1831644, 6217523, 20716164, 68059710, 221195824, 712856665, 2282058360, 7266358556, 23035517940, 72760054815, 229112753980, 719545590010, 2254604460264, 7050252659525, 22006821057936, 68581455012504, 213411502891468
OFFSET
3,2
COMMENTS
Exactly 2 adjacent element pairs in decreasing order gives A027540(n-1).
LINKS
Index entries for linear recurrences with constant coefficients, signature (16,-111,438,-1083,1740,-1817,1190,-444,72).
FORMULA
From Andrew Howroyd, May 05 2020: (Start)
a(n) = n*A000460(n-1).
a(n) = n*(3^(n-1) - n*2^(n-1) + n*(n-1)/2).
a(n) = 16*a(n-1) - 111*a(n-2) + 438*a(n-3) - 1083*a(n-4) + 1740*a(n-5) - 1817*a(n-6) + 1190*a(n-7) - 444*a(n-8) + 72*a(n-9).
G.f.: x^4*(4 - 9*x - 40*x^2 + 131*x^3 - 98*x^4)/((1 - x)^4*(1 - 2*x)^3*(1 - 3*x)^2).
(End)
PROG
(PARI) a(n)={n*(3^(n-1) - n*2^(n-1) + n*(n-1)/2)} \\ Andrew Howroyd, May 05 2020
CROSSREFS
Column k=3 of A334218.
Related sequences: A151577-A151610.
Cf. A000460.
Sequence in context: A352510 A133218 A190441 * A204107 A285366 A202163
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, May 21 2009
EXTENSIONS
Terms a(18) and beyond from Andrew Howroyd, May 05 2020
STATUS
approved