A151597 Number of permutations of 4 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.

0, 36, 606, 4744, 30850, 186924, 1092966, 6248976, 35154954, 195310900, 1074216814, 5859372696, 31738278546, 170898434364, 915527340150, 4882812495904, 25939941401626, 137329101557316, 724792480462974, 3814697265618600, 20027160644524194, 104904174804679756

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 (13,-58,106,-85,25).

Crossrefs

Cf. A151583.

Programs

Magma

[0] cat [ n*(2*5^n - 16*n) : n in [2..30]]; // Wesley Ivan Hurt, Jul 16 2020

PARI

a(n) = if(n <= 1, 0, n*(2*5^n - 16*n)) \\ Andrew Howroyd, May 04 2020

PARI

concat(0, Vec(2*x^2*(18 + 69*x - 523*x^2 + 255*x^3 - 75*x^4) / ((1 - x)^3*(1 - 5*x)^2) + O(x^40))) \\ Colin Barker, Jul 16 2020

Formula

a(n) = n*(2*5^n - 16*n) for n > 1. - Andrew Howroyd, May 04 2020

From Colin Barker, Jul 16 2020: (Start)

G.f.: 2*x^2*(18 + 69*x - 523*x^2 + 255*x^3 - 75*x^4) / ((1 - x)^3*(1 - 5*x)^2).

a(n) = 13*a(n-1) - 58*a(n-2) + 106*a(n-3) - 85*a(n-4) + 25*a(n-5) for n>6.

(End)

Extensions

Terms a(9) and beyond from Andrew Howroyd, May 04 2020