A203952 - OEIS

A203952

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203949.

1, -1, 1, -2, 1, 1, -3, 3, -1, 1, -4, 6, -4, 1, 1, -6, 13, -13, 6, -1, 1, -8, 24, -34, 24, -8, 1, 1, -10, 39, -75, 75, -39, 10, -1, 1, -12, 58, -144, 195, -144, 58, -12, 1, 1, -14, 81, -250, 444, -459, 271, -89, 15, -1, 1, -16, 108, -400, 886

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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...-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. A203951, A202605.

Sequence in context: A183328 A034328 A034253 * A296115 A118687 A281587

Adjacent sequences: A203949 A203950 A203951 * A203953 A203954 A203955

KEYWORD

tabf,sign

AUTHOR

Clark Kimberling, Jan 08 2012

STATUS

approved