login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A203948 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203947. 2
1, -1, 1, -2, 1, 1, -4, 4, -1, 1, -7, 13, -7, 1, 1, -11, 35, -31, 10, -1, 1, -16, 74, -107, 61, -14, 1, 1, -22, 147, -308, 275, -111, 19, -1, 1, -29, 256, -763, 1001, -629, 186, -24, 1, 1, -37, 428, -1683, 3013, -2721, 1264, -291, 30, -1, 1, -46 (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..56.

EXAMPLE

Top of the array:

1...-1

1...-2....1

1...-4....4....-1

1...-7....13...-7....1

1...-11...35...-31...10...-1

MATHEMATICA

t = {1, 0, 1}; t1 = Flatten[{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[%]

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

CROSSREFS

Cf. A203947, A202605.

Sequence in context: A118245 A104382 A086629 * A296990 A156184 A056588

Adjacent sequences:  A203945 A203946 A203947 * A203949 A203950 A203951

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 08 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 18 22:50 EST 2019. Contains 329305 sequences. (Running on oeis4.)