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A173820 Coefficients of characteristic polynomials of Hadamard Cartan F_2 self-similar 2^n matrices:M={{2, -1}, {-2, 2}}.

%I A173820 #2 Mar 30 2012 17:34:39
%S A173820 1,2,-4,1,16,-64,56,-16,1,4096,-32768,75776,-77824,39296,-9728,1184,
%T A173820 -64,1,4294967296,-68719476736,375809638400,-1043677052928,
%U A173820 1696981843968,-1726845288448,1143073669120,-506453819392,152912134144,-31653363712
%N A173820 Coefficients of characteristic polynomials of Hadamard Cartan F_2 self-similar 2^n matrices:M={{2, -1}, {-2, 2}}.
%C A173820 Row sums are:
%C A173820 {1, -1, -7, -31, -208289151, 199276356275696712709633,
%C A173820 -27294457550222463310332530871924308277403810665846783,...}.
%F A173820 M(2)={{2, -1}, {-2, 2}};
%F A173820 M(4)={{4, -2, -2, 1}, {-4, 4, 2, -2}, {-4, 2, 4, -2}, {4, -4, -4, 4}},etc.
%e A173820 {1},
%e A173820 {2, -4, 1},
%e A173820 { 16, -64, 56, -16, 1},
%e A173820 {4096, -32768, 75776, -77824, 39296, -9728, 1184, -64, 1}, ...
%t A173820 Clear[HadamardMatrix];
%t A173820 MatrixJoinH[A_, B_] := Transpose[Join[Transpose[A], Transpose[B]]]
%t A173820 KroneckerProduct[M_, N_] := Module[{M1, N1, LM, LN, N2},
%t A173820 M1 = M;
%t A173820 N1 = N;
%t A173820 LM = Length[M1];
%t A173820 LN = Length[N1];
%t A173820 Do[M1[[i, j]] = M1[[i, j]]N1, {i, 1, LM}, {j, 1, LM}];
%t A173820 Do[M1[[i, 1]] = MatrixJoinH[M1[[i, 1]], M1[[i, j]]], {j, 2, LM}, {i, 1, LM}];
%t A173820 N2 = {};
%t A173820 Do[AppendTo[N2, M1[[i, 1]]], {i, 1, LM}];
%t A173820 N2 = Flatten[N2];
%t A173820 Partition[N2, LM*LN, LM*LN]]
%t A173820 HadamardMatrix[2] := {{2, -1}, {-2, 2}}
%t A173820 HadamardMatrix[n_] := Module[{m},
%t A173820 m = {{2, -1}, {-2, 2}};
%t A173820 KroneckerProduct[m, HadamardMatrix[n/2]]]
%t A173820 Table[HadamardMatrix[2^n], {n, 1, 4}]
%t A173820 Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[ HadamardMatrix[2^n], x], x], {n, 1, 6}]]
%t A173820 Flatten[%]
%Y A173820 Cf. A136674, A158800, A173814, A136678
%K A173820 sign,tabl,uned
%O A173820 0,2
%A A173820 _Roger L. Bagula_, Feb 25 2010