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A173814 Coefficients of Hadamard Cartan G_2 self-similar 2^n matrices:M={{2, -1}, {-3, 2}} 1
1, 1, -4, 1, 1, -16, 30, -16, 1, 1, -64, 676, -2752, 4678, -2752, 676, -64, 1, 1, -256, 13560, -316160, 3830300, -25002240, 87841480, -180202240, 227671110, -180202240, 87841480, -25002240, 3830300, -316160, 13560, -256, 1, 1, -1024 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums are:

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

LINKS

Table of n, a(n) for n=0..36.

FORMULA

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

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

EXAMPLE

{1},

{1, -4, 1},

{1, -16, 30, -16, 1},

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

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

{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}, ...

MATHEMATICA

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

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

M1 = M;

N1 = N;

LM = Length[M1];

LN = Length[N1];

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

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

N2 = {};

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

N2 = Flatten[N2];

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

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

HadamardMatrix[n_] := Module[{m},

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

KroneckerProduct[m, HadamardMatrix[n/2]]]

Table[HadamardMatrix[2^n], {n, 1, 4}]

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

Flatten[%]

CROSSREFS

Cf. A136674, A158800

Sequence in context: A118185 A176483 A174639 * A176467 A034802 A177262

Adjacent sequences:  A173811 A173812 A173813 * A173815 A173816 A173817

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Feb 25 2010

STATUS

approved

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Last modified October 18 08:58 EDT 2021. Contains 348067 sequences. (Running on oeis4.)