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

1,2

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).

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)

Prog

(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

Crossrefs

Cf. A151583.

Sequence in context: A126861 A038727 A204476 * A199533 A333075 A323962

Adjacent sequences: A151600 A151601 A151602 * A151604 A151605 A151606

Keyword

nonn,easy

Author

R. H. Hardin, May 21 2009

Extensions

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

Status

approved