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A203954 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203953. 3
1, -1, 1, -6, 1, 1, -20, 12, -1, 1, -70, 75, -22, 1, 1, -264, 406, -200, 33, -1, 1, -1034, 2085, -1470, 430, -48, 1, 1, -4108, 10296, -9600, 4116, -816, 64, -1, 1, -16398, 49231, -57574, 33135, -9786, 1410, -84, 1, 1, -65552, 229482 (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..47.

EXAMPLE

Top of the array:

1...-1

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

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

1...-70....75....-22....1

1...-264...406...-200...33...-1

MATHEMATICA

t = {1, 2}; t1 = Flatten[{t, 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[%]  (* A203954 *)

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

CROSSREFS

Cf. A203953, A202605.

Sequence in context: A318408 A146957 A146988 * A060972 A144066 A296827

Adjacent sequences:  A203951 A203952 A203953 * A203955 A203956 A203957

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 08 2012

STATUS

approved

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Last modified January 26 06:32 EST 2021. Contains 340434 sequences. (Running on oeis4.)