%I #12 Sep 08 2022 08:45:06
%S 0,96,1560,20160,246840,2978976,35806680,429889920,5159439480,
%T 61916079456,743003467800,8916081545280,106993131892920,
%U 1283918176981536,15407020443448920,184884254427882240,2218611089044007160,26623333210616085216,319479999091095974040
%N Number of n-tuples of elements e_1,e_2,...,e_n in the alternating group A_4 such that the subgroup generated by e_1,e_2,...,e_n is A_4.
%H Andrew Howroyd, <a href="/A071765/b071765.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (20, -115, 240,-144).
%F G.f.: (-360x^2 + 96x) / (-144x^4 + 240x^3 - 115x^2 + 20x - 1).
%F G.f.: 24*x*(4 - 15*x)/((1 - x)*(1 - 3*x)*(1 - 4*x)*(1 - 12*x)). - _Andrew Howroyd_, Jul 04 2018
%F a(n) = 20*a(n-1) - 115*a(n-2) + 240*a(n-3) - 144*a(n-4). - _Vincenzo Librandi_, Jul 04 2018
%t LinearRecurrence[{20, -115, 240, -144}, {0, 96, 1560, 20160}, 40] (* _Vincenzo Librandi_, Jul 04 2018 *)
%o (PARI) concat([0], Vec(24*(4 - 15*x)/((1 - x)*(1 - 3*x)*(1 - 4*x)*(1 - 12*x)) + O(x^20))) \\ _Andrew Howroyd_, Jul 04 2018
%o (Magma) I:=[0,96,1560,20160]; [n le 4 select I[n] else 20*Self(n-1)- 115*Self(n-2)+240*Self(n-3)-144*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Jul 04 2018
%Y Cf. A071539.
%K nonn
%O 1,2
%A Sharon Sela (sharonsela(AT)hotmail.com), Jun 04 2002
%E Terms a(10) and beyond from _Andrew Howroyd_, Jul 04 2018