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%I #13 Sep 08 2022 08:44:50
%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(n-1)-144*a(n-2). - _Colin Barker_, May 28 2015
%F G.f.: -6*x*(20*x-1) / ((4*x-1)*(36*x-1)). - _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*x-1) / ((4*x-1)*(36*x-1)) + O(x^100)) \\ _Colin Barker_, May 28 2015
%K nonn,easy
%O 1,1
%A Paolo Dominici (pl.dm(AT)libero.it)
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