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A293147
Triangle read by rows: coefficients of the characteristic polynomial of the n-th submatrix of A191898.
1
0, 1, -1, -2, 0, 1, 6, 4, -2, -1, 0, -12, -5, 3, 1, 0, 60, 49, -3, -7, -1, 0, 360, 84, -90, -19, 5, 1, 0, -2520, -1308, 414, 241, -5, -11, -1, 0, 0, 3780, 1752, -590, -290, 9, 12, 1, 0, 0, 0, -7560, -2874, 1122, 406, -19, -14, -1
OFFSET
0,4
COMMENTS
It appears that for n > 10, the nearest integer to the largest negative eigenvalue of the n-th characteristic polynomial is equal to the previous prime sequence A007917(n).
A007917(n) = round(max(-eigenvalues(A191898(1..n,1..n)))) (for n > 10), has been verified in the range n=11 to n=100.
EXAMPLE
0;
1, -1;
-2, 0, 1;
6, 4, -2, -1;
0, -12, -5, 3, 1;
0, 60, 49, -3, -7, -1;
0, 360, 84, -90, -19, 5, 1;
0, -2520, -1308, 414, 241, -5, -11, -1;
0, 0, 3780, 1752, -590, -290, 9, 12, 1;
0, 0, 0, -7560, -2874, 1122, 406, -19, -14, -1;
...
max(-eigenvalues(A191898(1..12,1..12)))=11.096...
max(-eigenvalues(A191898(1..13,1..13)))=12.9021...
MATHEMATICA
Clear[A, B, nnn]; nnn=9; charpol = Table[A = Table[Table[If[Mod[n, k] == 0, 1, 0], {k, 1, nn}], {n, 1, nn}]; B = Table[Table[If[Mod[k, n] == 0, MoebiusMu[n]*n, 0], {k, 1, nn}], {n, 1, nn}]; CoefficientList[CharacteristicPolynomial[A.B, x], x], {nn, 1, nnn}]; Flatten[charpol]
CROSSREFS
Sequence in context: A289537 A323837 A114709 * A331047 A264550 A089949
KEYWORD
sign,tabl
AUTHOR
Mats Granvik, Oct 01 2017
STATUS
approved