A151597 - OEIS

%I #14 Sep 08 2022 08:45:38

%S 0,36,606,4744,30850,186924,1092966,6248976,35154954,195310900,

%T 1074216814,5859372696,31738278546,170898434364,915527340150,

%U 4882812495904,25939941401626,137329101557316,724792480462974,3814697265618600,20027160644524194,104904174804679756

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

%H Andrew Howroyd, <a href="/A151597/b151597.txt">Table of n, a(n) for n = 1..500</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (13,-58,106,-85,25).

%F a(n) = n*(2*5^n - 16*n) for n > 1. - _Andrew Howroyd_, May 04 2020

%F From _Colin Barker_, Jul 16 2020: (Start)

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

%F 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.

%F (End)

%o (Magma) [0] cat [ n*(2*5^n - 16*n) : n in [2..30]]; // _Wesley Ivan Hurt_, Jul 16 2020

%o (PARI) a(n) = if(n <= 1, 0, n*(2*5^n - 16*n)) \\ _Andrew Howroyd_, May 04 2020

%o (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

%Y Cf. A151583.

%K nonn,easy

%O 1,2

%A _R. H. Hardin_, May 21 2009

%E Terms a(9) and beyond from _Andrew Howroyd_, May 04 2020