A151658 Number of permutations of 8 indistinguishable copies of 1..n with exactly 2 adjacent element pairs in decreasing order.

0, 784, 73200, 3884640, 182107936, 8277726192, 373396825488, 16812327355840, 756652360885056, 34050346486482384, 1532275508306401840, 68952496159266606624, 3102863293076011859040, 139628857613659024861360, 6283298684030318768507856, 282748441663401954476011392

Offset: 1

Author

R. H. Hardin, May 29 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 (66,-1083,6508,-13671,11826,-3645).

Crossrefs

Cf. A151624.

Programs

PARI

a(n) = {45^n - (8*n + 1)*9^n + 4*n*(8*n + 1)} \\ Andrew Howroyd, May 06 2020

PARI

concat(0, Vec(16*x^2*(49 + 1341*x - 6093*x^2 - 6561*x^3) / ((1 - x)^3*(1 - 9*x)^2*(1 - 45*x)) + O(x^40))) \\ Colin Barker, Jul 19 2020

Formula

a(n) = 45^n - (8*n + 1)*9^n + 4*n*(8*n + 1). - Andrew Howroyd, May 06 2020

From Colin Barker, Jul 19 2020: (Start)

G.f.: 16*x^2*(49 + 1341*x - 6093*x^2 - 6561*x^3) / ((1 - x)^3*(1 - 9*x)^2*(1 - 45*x)).

a(n) = 66*a(n-1) - 1083*a(n-2) + 6508*a(n-3) - 13671*a(n-4) + 11826*a(n-5) - 3645*a(n-6) for n>6.

(End)

Extensions

Terms a(7) and beyond from Andrew Howroyd, May 06 2020