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%I #18 Sep 08 2022 08:45:15
%S 3,2,12,8,48,32,192,128,768,512,3072,2048,12288,8192,49152,32768,
%T 196608,131072,786432,524288,3145728,2097152,12582912,8388608,
%U 50331648,33554432,201326592,134217728,805306368,536870912,3221225472,2147483648
%N Trace sequence of 3 X 3 Krawtchouk matrix.
%C Let A=[1,1,1;2,0,-2;1,-1,1], the 3 X 3 Krawtchouk matrix. Then a(n)=trace(A^n).
%H Vincenzo Librandi, <a href="/A098646/b098646.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,4)
%F G.f.: (3+2*x)/((1+2*x)*(1-2*x)).
%F a(n) = (-2)^n+2*2^n.
%F Recurrence: a(n) = 4a(n-2), a(0)=3, a(1)=2. - _Ralf Stephan_, Jul 17 2013
%F a(2n+1)=A081294(n+1). a(2n)=A002001(n+1). - _R. J. Mathar_, Nov 11 2013
%o (Magma) [(-2)^n+2*2^n: n in [0..45]]; // _Vincenzo Librandi_, Jun 11 2011
%Y Cf. A074535, A098647.
%K easy,nonn
%O 0,1
%A _Paul Barry_, Sep 18 2004
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