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A203950 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203949. 4
1, -1, 1, -3, 1, 1, -6, 5, -1, 1, -13, 18, -8, 1, 1, -24, 52, -40, 12, -1, 1, -39, 131, -155, 78, -16, 1, 1, -58, 291, -508, 391, -138, 21, -1, 1, -81, 584, -1410, 1548, -840, 225, -27, 1, 1, -108, 1078, -3448, 5151, -4016, 1658, -348, 33, -1, 1 (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..55.

EXAMPLE

Top of the array:

1...-1

1...-3....1

1...-6....5....-1

1...-13....18...-8....1

1...-24...52...-40...12...-1

MATHEMATICA

t = {1, 1, 0}; 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}]  (* A203950 *)

Flatten[%]

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

CROSSREFS

Cf. A203949, A202605.

Sequence in context: A145904 A273350 A278132 * A273349 A159572 A190907

Adjacent sequences:  A203947 A203948 A203949 * A203951 A203952 A203953

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 08 2012

STATUS

approved

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Last modified September 15 12:22 EDT 2019. Contains 327078 sequences. (Running on oeis4.)