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 A158336 A triangle of matrix polynomials: m(n)=antisymmeticmatix(n).pseudotranspose[antisymmeticmatix(n)]. 0
 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, 1, 0, 49, 0, -931, 0, 371, 0, -1, 1, 0, -644, 0, 3334, 0, -644, 0, 1, 0, -81, 0, 4788, 0, -9846, 0, 1044, 0, -1, -1, 0, 1605, 0, -25290, 0, 25290, 0, -1605, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS The pseusotranspose operation used is: pseudotranspose[a(n)]=Reverse[I(n)].a(n). Row sums are: {1, -1, 0, 8, -32, 64, 0, -512, 2048, -4096, 0,...}. Unsigned row sums are: {1, 1, 2, 10, 36, 116, 392, 1352, 4624, 15760, 53792,...}. Example matrix is: M(3)={{-1, -1, 2}, {-1, 2, -1}, {2, -1, -1}} LINKS FORMULA m(n)=antisymmeticmatix(n).pseudotranspose[antisymmeticmatix(n)].; out_(n,m)=coefficients(characteristicpolynomial(m(n),x),x). EXAMPLE {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, 1}, {0, 49, 0, -931, 0, 371, 0, -1}, {1, 0, -644, 0, 3334, 0, -644, 0, 1}, {0, -81, 0, 4788, 0, -9846, 0, 1044, 0, -1}, {-1, 0, 1605, 0, -25290, 0, 25290, 0, -1605, 0, 1} MATHEMATICA Clear[M, T, d, a, x, a0]; pt[a_] := Reverse[IdentityMatrix[Length[a]]].a; T[n_, m_, d_] := If[ m < n, (-1)^(n + m), If[m > n, -(-1)^(n + m), 0]]; 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}]]; Table[Det[M[d]], {d, 1, 10}]; Table[M[d], {d, 1, 10}] Table[CharacteristicPolynomial[M[d], x], {d, 1, 10}]; a = Join[{{1}}, Table[CoefficientList[Expand[CharacteristicPolynomial[M[ n], x]], x], {n, 1, 10}]]; Flatten[a]; Join[{1}, Table[Apply[Plus, CoefficientList[Expand[ CharacteristicPolynomial[M[n], x]], x]], {n, 1, 10}]]; CROSSREFS Sequence in context: A221804 A275107 A274186 * A021530 A272232 A110909 Adjacent sequences:  A158333 A158334 A158335 * A158337 A158338 A158339 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Mar 16 2009 STATUS approved

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Last modified April 7 10:46 EDT 2020. Contains 333301 sequences. (Running on oeis4.)