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A203002
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Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of the symmetric matrix A203001; by antidiagonals.
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2
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1, -1, 1, -3, 1, 1, -14, 21, -1, 1, -29, 162, -120, 1, 1, -48, 540, -1736, 844, -1, 1, -71, 1267, -8091, 17022, -5664, 1, 1, -98, 2475, -24908, 105503, -158690, 39045, -1, 1, -129, 4312, -60994, 408508, -1250056, 1416673
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OFFSET
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1,4
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COMMENTS
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Let p(n)=p(n,x) be the characteristic polynomial of the n-th principal submatrix. The zeros of p(n) are positive, and they interlace the zeros of p(n+1).
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LINKS
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EXAMPLE
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Top of the array:
1...-1
1...-3....1
1...-14...21....-1
1...-29...162...-120...1
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MATHEMATICA
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f[k_] := Fibonacci[k]^2;
U[n_] := NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[f[k], {k, 1, n}]];
L[n_] := Transpose[U[n]];
F[n_] := CharacteristicPolynomial[L[n].U[n], x];
c[n_] := CoefficientList[F[n], x]
TableForm[Flatten[Table[F[n], {n, 1, 10}]]]
Table[c[n], {n, 1, 12}]
Flatten[%]
TableForm[Table[c[n], {n, 1, 10}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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