A151576 Number of permutations of 1..n arranged in a circle with exactly 3 adjacent element pairs in decreasing order.

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

Andrew Howroyd, Table of n, a(n) for n = 3..500

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

Adjacent sequences: A151573 A151574 A151575 * A151577 A151578 A151579

Keyword

nonn,easy

Author

R. H. Hardin, May 21 2009

Extensions

Terms a(18) and beyond from Andrew Howroyd, May 05 2020

Status

approved