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A204011 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max{3i+j-3,i+3j-3} (A204008). 3
1, -1, -11, -6, 1, 40, 70, 15, -1, -116, -328, -240, -28, 1, 304, 1176, 1456, 610, 45, -1, -752, -3680, -6408, -4704, -1295, -66, 1, 1792, 10592, 23760, 25080, 12432, 2436, 91, -1, -4160, -28800, -79040 (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 for a guide to related sequences.

REFERENCES

(For references regarding interlacing roots, see A202605.)

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

Top of the array:

1.....-1

-11....-6.....1

40.....70....15....-1

-116...-328..-240....1

MATHEMATICA

f[i_, j_] := Max[3 i + j - 3, 3 j + i - 3];

m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

TableForm[m[6]] (* 6x6 principal submatrix *)

Flatten[Table[f[i, n + 1 - i],

{n, 1, 12}, {i, 1, n}]]   (* A204008 *)

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[%]                (* A204011 *)

TableForm[Table[c[n], {n, 1, 10}]]

CROSSREFS

Cf. A204008, A202605.

Sequence in context: A002547 A090840 A227775 * A288069 A236175 A193813

Adjacent sequences:  A204008 A204009 A204010 * A204012 A204013 A204014

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 09 2012

STATUS

approved

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Last modified April 18 15:05 EDT 2019. Contains 322209 sequences. (Running on oeis4.)