A071765 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.

0, 96, 1560, 20160, 246840, 2978976, 35806680, 429889920, 5159439480, 61916079456, 743003467800, 8916081545280, 106993131892920, 1283918176981536, 15407020443448920, 184884254427882240, 2218611089044007160, 26623333210616085216, 319479999091095974040

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (20,-115,240,-144).

Formula

G.f.: (360*x^3 - 96*x^2) / (-144*x^4 + 240*x^3 - 115*x^2 + 20*x - 1).

G.f.: 24*x^2*(4 - 15*x)/((1 - x)*(1 - 3*x)*(1 - 4*x)*(1 - 12*x)). - Andrew Howroyd, Jul 04 2018

a(n) = 20*a(n-1) - 115*a(n-2) + 240*a(n-3) - 144*a(n-4). - Vincenzo Librandi, Jul 04 2018

a(n) = 12^n - 4^n - 4*3^n + 4 = (3^n-1)*(4^n-4). - Christian Krause, May 06 2026

Mathematica

LinearRecurrence[{20, -115, 240, -144}, {0, 96, 1560, 20160}, 30] (* Vincenzo Librandi, Jul 04 2018 *)

Prog

(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
(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

Crossrefs

Cf. A071539.

Sequence in context: A223292 A168526 A128962 * A064243 A001667 A093984

Adjacent sequences: A071762 A071763 A071764 * A071766 A071767 A071768

Keyword

nonn,easy

Author

Sharon Sela (sharonsela(AT)hotmail.com), Jun 04 2002

Extensions

Terms a(10) and beyond from Andrew Howroyd, Jul 04 2018

Status

approved