A158452 A triangle sequence of permutation Hadamard {1,-1) matrix polynomials: M(d)=Table[If[ m == n, d!/n!, 0], {n, d}, {m, d}]; m(n)=M(2^n)*Hadamard(2^n)

1, 2, 2, 1, -1, 24, 24, 24, 24, 12, -12, 12, -12, 4, -4, -4, 4, 1, 1, -1, -1, 40320, 40320, 40320, 40320, 40320, 40320, 40320, 40320, 20160, -20160, -20160, -20160, 20160, 20160, -20160, 20160, 6720, 6720, -6720, -6720, -6720, -6720, 6720, 6720, 1680

Offset

0,2

Comments

Row sums are:

{0, -4, -25078, -6495526469206231383391390,

286062680268501848545408513842882834075841335269461890307160415945609971775008

5331640349522681828065666242531221092072696301456782016,...}.

Example matrix:

m(2^2)={{24, 24, 24, 24},

{12, -12, 12, -12},

{4, -4, -4, 4},

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

Links

Table of n, a(n) for n=0..45.

Formula

M(d)=Table[If[ m == n, d!/n!, 0], {n, d}, {m, d}];

m(n)=M(2^n)*Hadamard(2^n);

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

Example

{1, -1},
{-4, -1, 1},
{-18432, -5952, -688, -7, 1},

Mathematica

Needs["Hadamard`"];
M[d_] := Table[If[ m == n, d!/n!, 0], {n, d}, {m, d}];
a = Join[{{{1}}}, Table[M[2^n].If[Hadamard[2^n] == {} && 2^n >= 3, 0, If[2^n == 2, Hadamard[2], Hadamard[2^n][[1]]]], {n, 1, 4}]];
Table[CoefficientList[CharacteristicPolynomial[a[[n]], x], x], {n, 1, Length[ a]}];
Flatten[a]
Table[Apply[Plus, CoefficientList[CharacteristicPolynomial[a[[n]], x], x]], {n, 1, Length[a]}];

Crossrefs

Sequence in context: A174120 A240939 A016739 * A208929 A039965 A300481

Adjacent sequences: A158449 A158450 A158451 * A158453 A158454 A158455

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Mar 19 2009

Status

approved