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 A204155 Array read by rows: row n lists the coefficients of the characteristic polynomial of the n-th principal submatrix of max(2i-j, 2j-i), as in A204154. 3
 1, -1, -7, -3, 1, 33, 39, 6, -1, -135, -255, -125, -10, 1, 513, 1323, 1092, 305, 15, -1, -1863, -6075, -7047, -3444, -630, -21, 1, 6561, 25839, 38610, 27135, 8946, 1162, 28, -1, -22599, -104247, -190593, -175230 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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 Robert Israel, Table of n, a(n) for n = 1..10010 (rows 1 to 140, flattened) EXAMPLE Top of the array: 1, -1; -7, -3, 1; 33, 39, 6, -1; -135, -255, -125, -10, 1; MAPLE f:= proc(n) local P, lambda, i; P:= (-1)^n*LinearAlgebra:-CharacteristicPolynomial(Matrix(n, n, (i, j) -> max(2*i-j, 2*j-i)), lambda); seq(coeff(P, lambda, i), i=0..n); end proc: map(f, [\$1..20]); # Robert Israel, Dec 03 2017 MATHEMATICA f[i_, j_] := Max[2 i - j, 2 j - i]; 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}]] (* A204154 *) 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[%] (* A204155 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204154, A202605, A204016. Sequence in context: A021899 A176435 A133722 * A363232 A355673 A160390 Adjacent sequences: A204152 A204153 A204154 * A204156 A204157 A204158 KEYWORD tabl,sign,look AUTHOR Clark Kimberling, Jan 12 2012 STATUS approved

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Last modified June 4 09:12 EDT 2023. Contains 363121 sequences. (Running on oeis4.)