A158336 - OEIS

%I #2 Mar 30 2012 17:34:35

%S 1,0,-1,-1,0,1,0,9,0,-1,1,0,-34,0,1,0,-25,0,90,0,-1,-1,0,195,0,-195,0,

%T 1,0,49,0,-931,0,371,0,-1,1,0,-644,0,3334,0,-644,0,1,0,-81,0,4788,0,

%U -9846,0,1044,0,-1,-1,0,1605,0,-25290,0,25290,0,-1605,0,1

%N A triangle of matrix polynomials: m(n)=antisymmeticmatix(n).pseudotranspose[antisymmeticmatix(n)].

%C The pseusotranspose operation used is: pseudotranspose[a(n)]=Reverse[I(n)].a(n).

%C Row sums are:

%C {1, -1, 0, 8, -32, 64, 0, -512, 2048, -4096, 0,...}. Unsigned row sums are:

%C {1, 1, 2, 10, 36, 116, 392, 1352, 4624, 15760, 53792,...}.

%C Example matrix is:

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

%C {-1, 2, -1},

%C {2, -1, -1}}

%F m(n)=antisymmeticmatix(n).pseudotranspose[antisymmeticmatix(n)].;

%F out_(n,m)=coefficients(characteristicpolynomial(m(n),x),x).

%e {1},

%e {0, -1},

%e {-1, 0, 1},

%e {0, 9, 0, -1},

%e {1, 0, -34, 0, 1},

%e {0, -25, 0, 90, 0, -1},

%e {-1, 0, 195, 0, -195, 0, 1},

%e {0, 49, 0, -931, 0, 371, 0, -1},

%e {1, 0, -644, 0, 3334, 0, -644, 0, 1},

%e {0, -81, 0, 4788, 0, -9846, 0, 1044, 0, -1},

%e {-1, 0, 1605, 0, -25290, 0, 25290, 0, -1605, 0, 1}

%t Clear[M, T, d, a, x, a0];

%t pt[a_] := Reverse[IdentityMatrix[Length[a]]].a;

%t T[n_, m_, d_] := If[ m < n, (-1)^(n + m), If[m > n, -(-1)^(n + m), 0]];

%t M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}].pt[Table[T[ n, m, d], {n, 1, d}, {m, 1, d}]];

%t Table[Det[M[d]], {d, 1, 10}];

%t Table[M[d], {d, 1, 10}]

%t Table[CharacteristicPolynomial[M[d], x], {d, 1, 10}];

%t a = Join[{{1}}, Table[CoefficientList[Expand[CharacteristicPolynomial[M[ n], x]], x], {n, 1, 10}]];

%t Flatten[a]; Join[{1}, Table[Apply[Plus, CoefficientList[Expand[ CharacteristicPolynomial[M[n], x]], x]], {n, 1, 10}]];

%Y A119467

%K sign,tabl,uned

%O 0,8

%A _Roger L. Bagula_, Mar 16 2009