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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 * A160390 A002194 A256843

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 October 16 13:19 EDT 2019. Contains 328082 sequences. (Running on oeis4.)