A151607 Number of permutations of 6 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.

0, 150, 2763, 28236, 251205, 2116386, 17292639, 138352920, 1089544473, 8474253870, 65251778163, 498286334052, 3778671399789, 28485369052602, 213640267939335, 1595180667331632, 11864156213337153, 87934334287152582, 649737025566256155, 4787535977856705660

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 (17,-94,190,-161,49).

Crossrefs

Cf. A151583.

Programs

PARI

a(n) = if(n <= 1, 0, n*(3*7^n - 36*n)) \\ Andrew Howroyd, May 04 2020

PARI

concat(0, Vec(3*x^2*(50 + 71*x - 1545*x^2 + 805*x^3 - 245*x^4) / ((1 - x)^3*(1 - 7*x)^2) + O(x^40))) \\ Colin Barker, Jul 17 2020

Formula

a(n) = n*(3*7^n - 36*n) for n > 1. - Andrew Howroyd, May 04 2020

From Colin Barker, Jul 17 2020: (Start)

G.f.: 3*x^2*(50 + 71*x - 1545*x^2 + 805*x^3 - 245*x^4) / ((1 - x)^3*(1 - 7*x)^2).

a(n) = 17*a(n-1) - 94*a(n-2) + 190*a(n-3) - 161*a(n-4) + 49*a(n-5) for n>6.

(End)

Extensions

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