A151603 Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.

0, 80, 1395, 12560, 96575, 698940, 4897655, 33590720, 226746135, 1511651900, 9976916015, 65303466480, 424472551295, 2742745738460, 17631936915975, 112844396291840, 719383026394055, 4570198050070620, 28944587650489535, 182807922003138800, 1151689908619826415

Offset: 1

Author

R. H. Hardin, May 21 2009

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (15,-75,145,-120,36).

Crossrefs

Cf. A151583.

Programs

Magma

[0] cat [n*((5/2)*6^n - 25*n) : n in [2..30]]; // Wesley Ivan Hurt, Jul 17 2020

PARI

a(n) = if(n <= 1, 0, n*(5*6^n/2 - 25*n)) \\ Andrew Howroyd, May 04 2020

PARI

Vec(5*x^2*(16 + 39*x - 473*x^2 + 240*x^3 - 72*x^4) / ((1 - x)^3*(1 - 6*x)^2) + O(x^21)) \\ Colin Barker, Jul 17 2020

Formula

a(n) = n*((5/2)*6^n - 25*n) for n > 1. - Andrew Howroyd, May 04 2020

From Colin Barker, Jul 17 2020: (Start)

G.f.: 5*x^2*(16 + 39*x - 473*x^2 + 240*x^3 - 72*x^4) / ((1 - x)^3*(1 - 6*x)^2).

a(n) = 15*a(n-1) - 75*a(n-2) + 145*a(n-3) - 120*a(n-4) + 36*a(n-5) for n>5.

(End)

Extensions

Terms a(7) and beyond from Andrew Howroyd, May 04 2020