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 A029697 Number of words of length 2n in the 6 transpositions of S[ 4 ] equivalent to the identity. 1

%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(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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Last modified December 9 17:18 EST 2019. Contains 329879 sequences. (Running on oeis4.)