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 A173814 Coefficients of Hadamard Cartan G_2 self-similar 2^n matrices:M={{2, -1}, {-3, 2}} 1

%I

%S 1,1,-4,1,1,-16,30,-16,1,1,-64,676,-2752,4678,-2752,676,-64,1,1,-256,

%T 13560,-316160,3830300,-25002240,87841480,-180202240,227671110,

%U -180202240,87841480,-25002240,3830300,-316160,13560,-256,1,1,-1024

%N Coefficients of Hadamard Cartan G_2 self-similar 2^n matrices:M={{2, -1}, {-3, 2}}

%C Row sums are:

%C {1, -2, 0, 400, 0, 231040000000000, 0,...}.

%F M(2)={{2, -1}, {-3, 2}};

%F M(4)={{4, -2, -2, 1}, {-6, 4, 3, -2}, {-6, 3, 4, -2}, {9, -6, -6, 4}},etc.

%e {1},

%e {1, -4, 1},

%e {1, -16, 30, -16, 1},

%e {1, -64, 676, -2752, 4678, -2752, 676, -64, 1},

%e {1, -256, 13560, -316160, 3830300, -25002240, 87841480, -180202240, 227671110, -180202240, 87841480, -25002240, 3830300, -316160, 13560, -256, 1},

%e {1, -1024, 255376, -30325760, 2060069240, -86239093760, 2306160223920, -40571580718080, 489632650203420, -4209374685189120, 26512089196724880, -124638699726597120, 442120325884773960, -1188638208146519040, 2420933452415430960, -3721572797083978752, 4298314898249481798, -3721572797083978752, 2420933452415430960, -1188638208146519040, 442120325884773960, -124638699726597120, 26512089196724880, -4209374685189120, 489632650203420, -40571580718080, 2306160223920, -86239093760, 2060069240, -30325760, 255376, -1024, 1}, ...

%t MatrixJoinH[A_, B_] := Transpose[Join[Transpose[A], Transpose[B]]]

%t KroneckerProduct[M_, N_] := Module[{M1, N1, LM, LN, N2},

%t M1 = M;

%t N1 = N;

%t LM = Length[M1];

%t LN = Length[N1];

%t Do[M1[[i, j]] = M1[[i, j]]N1, {i, 1, LM}, {j, 1, LM}];

%t Do[M1[[i, 1]] = MatrixJoinH[M1[[i, 1]], M1[[i, j]]], {j, 2, LM}, {i, 1, LM}];

%t N2 = {};

%t Do[AppendTo[N2, M1[[i, 1]]], {i, 1, LM}];

%t N2 = Flatten[N2];

%t Partition[N2, LM*LN, LM*LN]]

%t HadamardMatrix[2] := {{2, -1}, {-3, 2}}

%t m = {{2, -1}, {-3, 2}};

%t Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[ HadamardMatrix[2^n], x], x], {n, 1, 6}]]

%t Flatten[%]

%Y Cf. A136674, A158800

%K sign,tabl,uned

%O 0,3

%A _Roger L. Bagula_, Feb 25 2010

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Last modified December 2 12:01 EST 2021. Contains 349440 sequences. (Running on oeis4.)