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 A204183 Symmetric matrix based on f(i,j) defined by f(i,1)=f(1,j)=1; f(i,i)= (-1)^(i-1); f(i,j)=0 otherwise; by antidiagonals. 3
 1, 1, 1, 1, -1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1 COMMENTS A204183 represents the matrix M given by f(i,j) for i>=1 and j>=1.  See A204184 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M. LINKS EXAMPLE Northwest corner: 1...1...1...1...1...1 1..-1...0...0...0...0 1...0...1...0...0...0 1...0...0..-1...0...0 1...0...0...0...1...0 MATHEMATICA f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1; f[i_, i_] := (-1)^(i - 1); m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}] TableForm[m[8]] (* 8x8 principal submatrix *) Flatten[Table[f[i, n + 1 - i],   {n, 1, 15}, {i, 1, n}]]  (* A204183 *) p[n_] := CharacteristicPolynomial[m[n], x]; c[n_] := CoefficientList[p[n], x] TableForm[Flatten[Table[p[n], {n, 1, 10}]]] Table[c[n], {n, 1, 12}] Flatten[%]                 (* A204184 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204184, A204016, A202453. Sequence in context: A014163 A308016 A166360 * A204177 A185917 A143104 Adjacent sequences:  A204180 A204181 A204182 * A204184 A204185 A204186 KEYWORD sign,tabl AUTHOR Clark Kimberling, Jan 12 2012 STATUS approved

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Last modified May 26 11:30 EDT 2022. Contains 354086 sequences. (Running on oeis4.)