login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A173820 Coefficients of characteristic polynomials of Hadamard Cartan F_2 self-similar 2^n matrices:M={{2, -1}, {-2, 2}}. 0
1, 2, -4, 1, 16, -64, 56, -16, 1, 4096, -32768, 75776, -77824, 39296, -9728, 1184, -64, 1, 4294967296, -68719476736, 375809638400, -1043677052928, 1696981843968, -1726845288448, 1143073669120, -506453819392, 152912134144, -31653363712 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are:

{1, -1, -7, -31, -208289151, 199276356275696712709633,

-27294457550222463310332530871924308277403810665846783,...}.

LINKS

Table of n, a(n) for n=0..27.

FORMULA

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

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

EXAMPLE

{1},

{2, -4, 1},

{ 16, -64, 56, -16, 1},

{4096, -32768, 75776, -77824, 39296, -9728, 1184, -64, 1}, ...

MATHEMATICA

Clear[HadamardMatrix];

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}, {-2, 2}}

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

m = {{2, -1}, {-2, 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, A173814, A136678

Sequence in context: A172385 A224783 A214058 * A030043 A045497 A117258

Adjacent sequences:  A173817 A173818 A173819 * A173821 A173822 A173823

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Feb 25 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 23 17:12 EST 2014. Contains 249851 sequences.