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

Author

R. H. Hardin, May 21 2009

Keywords

• nonn
• easy

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).

Crossrefs

Column k=3 of A334218.

Related sequences: A151577-A151610.

Cf. A000460.

Programs

PARI

a(n)={n*(3^(n-1) - n*2^(n-1) + n*(n-1)/2)} \\ Andrew Howroyd, May 05 2020

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)

Extensions

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