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A158336 A triangle of matrix polynomials: m(n)=antisymmeticmatix(n).pseudotranspose[antisymmeticmatix(n)].

%I A158336 #2 Mar 30 2012 17:34:35
%S A158336 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 A158336 1,0,49,0,-931,0,371,0,-1,1,0,-644,0,3334,0,-644,0,1,0,-81,0,4788,0,
%U A158336 -9846,0,1044,0,-1,-1,0,1605,0,-25290,0,25290,0,-1605,0,1
%N A158336 A triangle of matrix polynomials: m(n)=antisymmeticmatix(n).pseudotranspose[antisymmeticmatix(n)].
%C A158336 The pseusotranspose operation used is: pseudotranspose[a(n)]=Reverse[I(n)].a(n).
%C A158336 Row sums are:
%C A158336 {1, -1, 0, 8, -32, 64, 0, -512, 2048, -4096, 0,...}. Unsigned row sums are:
%C A158336 {1, 1, 2, 10, 36, 116, 392, 1352, 4624, 15760, 53792,...}.
%C A158336 Example matrix is:
%C A158336 M(3)={{-1, -1, 2},
%C A158336 {-1, 2, -1},
%C A158336 {2, -1, -1}}
%F A158336 m(n)=antisymmeticmatix(n).pseudotranspose[antisymmeticmatix(n)].;
%F A158336 out_(n,m)=coefficients(characteristicpolynomial(m(n),x),x).
%e A158336 {1},
%e A158336 {0, -1},
%e A158336 {-1, 0, 1},
%e A158336 {0, 9, 0, -1},
%e A158336 {1, 0, -34, 0, 1},
%e A158336 {0, -25, 0, 90, 0, -1},
%e A158336 {-1, 0, 195, 0, -195, 0, 1},
%e A158336 {0, 49, 0, -931, 0, 371, 0, -1},
%e A158336 {1, 0, -644, 0, 3334, 0, -644, 0, 1},
%e A158336 {0, -81, 0, 4788, 0, -9846, 0, 1044, 0, -1},
%e A158336 {-1, 0, 1605, 0, -25290, 0, 25290, 0, -1605, 0, 1}
%t A158336 Clear[M, T, d, a, x, a0];
%t A158336 pt[a_] := Reverse[IdentityMatrix[Length[a]]].a;
%t A158336 T[n_, m_, d_] := If[ m < n, (-1)^(n + m), If[m > n, -(-1)^(n + m), 0]];
%t A158336 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 A158336 Table[Det[M[d]], {d, 1, 10}];
%t A158336 Table[M[d], {d, 1, 10}]
%t A158336 Table[CharacteristicPolynomial[M[d], x], {d, 1, 10}];
%t A158336 a = Join[{{1}}, Table[CoefficientList[Expand[CharacteristicPolynomial[M[ n], x]], x], {n, 1, 10}]];
%t A158336 Flatten[a]; Join[{1}, Table[Apply[Plus, CoefficientList[Expand[ CharacteristicPolynomial[M[n], x]], x]], {n, 1, 10}]];
%Y A158336 A119467
%K A158336 sign,tabl,uned
%O A158336 0,8
%A A158336 _Roger L. Bagula_, Mar 16 2009