%I
%S 6,120,3936,140160,5039616,181401600,6530359296,235092541440,
%T 8463329918976,304679870791680,10968475323334656,394865111539384320,
%U 14215144015015182336,511745184538935951360,18422826643395251798016,663221759162203294924800
%N Number of words of length 2n in the 6 transpositions of S[ 4 ] equivalent to the identity.
%H Vincenzo Librandi, <a href="/A029697/b029697.txt">Table of n, a(n) for n = 1..300</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (40,144).
%F a(n) = (9*4^n+36^n)/12.
%F a(n) = 40*a(n1)144*a(n2).  _Colin Barker_, May 28 2015
%F G.f.: 6*x*(20*x1) / ((4*x1)*(36*x1)).  _Colin Barker_, May 28 2015
%o (MAGMA) [(9*4^n+36^n)/12: n in [1..15]]; // _Vincenzo Librandi_, Jun 30 2011
%o (PARI) Vec(6*x*(20*x1) / ((4*x1)*(36*x1)) + O(x^100)) \\ _Colin Barker_, May 28 2015
%K nonn,easy
%O 1,1
%A Paolo Dominici (pl.dm(AT)libero.it)
