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%I #10 Jun 13 2015 00:51:32
%S 1,12,224,4608,96256,2015232,42205184,883949568,18513657856,
%T 387755016192,8121246285824,170093589823488,3562486393470976,
%U 74613683694600192,1562729279488262144,32730226951263879168
%N Trace sequence associated to the 4 X 4 Krawtchouk matrix and its transpose.
%C Let A=[1,1,1,1;3,1,-1,-3;3,-1,-1,3;1,-1,1,-1], the 4 X 4 Krawtchouk matrix. Then a(n)=trace((A*A')^n)/4.
%C Twelfth binomial transform of ((4*sqrt(5))^n +(-4*sqrt(5))^n)/2, with g.f. 1/(1-80*x^2).
%H Vincenzo Librandi, <a href="/A098647/b098647.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (24,-64).
%F G.f.: (1-12*x)/(1-24*x+64*x^2).
%F a(n) = ((12+4*sqrt(5))^n+(12-4*sqrt(5))^n)/2.
%F a(n) = 2^(n-1)*((sqrt(5)-1)^(2*n)+(sqrt(5)+1)^(2*n)).
%F a(n) = 4^n*A098648(n). - _R. J. Mathar_, Nov 11 2013
%Y Cf. A098646.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Sep 18 2004
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