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 A204111 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j) = gcd(i+1, j+1) (A204030). 3
 2, -1, 5, -5, 1, 10, -20, 9, -1, 44, -100, 62, -14, 1, 104, -328, 330, -128, 20, -1, 656, -2208, 2476, -1176, 263, -27, 1, 2624, -10144, 13992, -8880, 2804, -452, 35, -1, 15744, -66112, 102384, -75760, 29512, -6336, 744, -44, 1, 67584 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let p(n)=p(n,x) be the characteristic polynomial of the n-th principal submatrix. The zeros of p(n) are real, and they interlace the zeros of p(n+1). See A202605 and A204016 for guides to related sequences. REFERENCES (For references regarding interlacing roots, see A202605.) LINKS Table of n, a(n) for n=1..45. EXAMPLE Top of the array: 2, -1; 5, -5, 1; 10, -20, 9, -1; 44, -100, 62, -14, 1; MATHEMATICA f[i_, j_] := GCD[i + 1, j + 1]; m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}] TableForm[m[8]] (* 8 X 8 principal submatrix *) Flatten[Table[f[i, n + 1 - i], {n, 1, 15}, {i, 1, n}]] (* A204030 *) 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[%] (* A204111 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204030, A202605, A204016. Sequence in context: A209695 A033282 A126350 * A079502 A209164 A209148 Adjacent sequences: A204108 A204109 A204110 * A204112 A204113 A204114 KEYWORD tabl,sign AUTHOR Clark Kimberling, Jan 11 2012 STATUS approved

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Last modified February 29 18:12 EST 2024. Contains 370428 sequences. (Running on oeis4.)