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A203956 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203955. 3
1, -1, 1, -6, 1, 1, -12, 20, -1, 1, -27, 165, -35, 1, 1, -123, 1255, -511, 54, -1, 1, -300, 9266, -6003, 1197, -82, 1, 1, -558, 77523, -71564, 20779, -2463, 111, -1, 1, -2841, 688624, -817771, 315489, -54393, 4386, -144, 1, 1, -9093 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Let p(n)=p(n,x) be the characteristic polynomial of the n-th principal submatrix.  The zeros of p(n) are positive, 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..46.

EXAMPLE

Top of the array:

1...-1

1...-6....1

1...-12....20....-1

1...-27....165...-35....1

1...-123...1255..-511...54...-1

MATHEMATICA

t = {1, 2, 3}; t1 = Flatten[{t, t, t, t, t, t, t, t, t}];

f[k_] := t1[[k]];

U[n_] :=

  NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[

   Table[f[k], {k, 1, n}]];

L[n_] := Transpose[U[n]];

p[n_] := CharacteristicPolynomial[L[n].U[n], x];

c[n_] := CoefficientList[p[n], x]

TableForm[Flatten[Table[p[n], {n, 1, 10}]]]

Table[c[n], {n, 1, 12}]

Flatten[%]  (* A203956 *)

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

CROSSREFS

Cf. A203955, A202605.

Sequence in context: A174150 A202673 A202875 * A082105 A230073 A143210

Adjacent sequences:  A203953 A203954 A203955 * A203957 A203958 A203959

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 08 2012

STATUS

approved

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Last modified April 6 12:08 EDT 2020. Contains 333273 sequences. (Running on oeis4.)