0,4

Row sums are:

{1, 1, -1, -21, -9317, -8353125, 4992309225,...}.

The program uses an add on :

Hadamard.m

downloaded at: http://ftp2.de.freebsd.org/pub/math/mathematica/math-source/Applications/Mathematics/Applied/0205-760/Hadamard.m

This method gives random solutions for higher Hadamard matrices

without the matrix self-similar qualification.

Example matrix: Hadamard[12][[1]]={{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},

{1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1},

{1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1},

{1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1},

{1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1},

{1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1},

{1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1},

{1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1},

{1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1},

{1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1},

{1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1},

{ 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1}}

M(n)=Hadamard[2^n] with 12 added;

out_(n,m)=coefficients(characteristicpolynomial(M(n),x),x).

{1},

{0, 1},

{-2, 0, 1},

{-16, -8, 0, 2, 1},

{-4096, -3072, -1792, -448, 0, 56, 28, 6, 1},

{-2985984, -2488320, -1824768, -760320, -253440, -46464, 0, 3872, 1760, 440, 88, 10, 1},

{4294967296, 0, 671088640, 0, 29360128, 0, -2752512, 0, -344064, 0, -10752, 0, 448, 0, 40, 0, 1}

Needs["Hadamard`"];

Table[If[Hadamard[n] == {} && n >= 3, 0, If[n == 2, Hadamard[2], Hadamard[n][[1]]]], {n, 1, 10}];

a = Join[{1}, {x}, Union[ Table[CharacteristicPolynomial[If[Hadamard[n] == {} && n >= 3, 0, If[n == 2, Hadamard[2], Hadamard[n][[1]]]], x], {n, 2, 16}]]];

Table[CoefficientList[a[[n]], x], {n, 1, Length[a] - 1}];

Flatten[%]

Table[Apply[Plus, CoefficientList[a[[n]], x]], {n, 1, Length[a] - 1}];

Sequence in context: A091803 A123002 A137514 this_sequence A069845 A091397 A119818

Adjacent sequences: A158231 A158232 A158233 this_sequence A158235 A158236 A158237

sign,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 14 2009