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A203946 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203945. 3
1, -1, 1, -2, 1, 1, -3, 3, -1, 1, -5, 8, -5, 1, 1, -7, 17, -17, 7, -1, 1, -9, 30, -45, 30, -9, 1, 1, -11, 47, -98, 103, -52, 12, -1, 1, -13, 68, -183, 269, -212, 83, -15, 1, 1, -15, 93, -308, 588, -651, 399, -123, 18, -1, 1, -17, 122, -481, 1136 (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..59.

EXAMPLE

Top of the array:

1...-1

1...-2....1

1...-3....3....-1

1...-5....8....-5....1

1...-7....17...-17...7...-1

MATHEMATICA

t = {1, 0, 0}; 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[%]   (* A203946 *)

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

CROSSREFS

Cf. A203945, A202605.

Sequence in context: A089980 A181031 A214987 * A128545 A194672 A034364

Adjacent sequences:  A203943 A203944 A203945 * A203947 A203948 A203949

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 08 2012

STATUS

approved

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Last modified November 14 10:20 EST 2019. Contains 329111 sequences. (Running on oeis4.)