login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A204124 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j) = gcd(2^(i-1), 2^(j-1)) (A144464). 3
1, -1, -3, -2, 1, -1, 11, 3, -1, 6, -6, -29, -4, 1, 1, -13, 8, 56, 5, -1, -1, -6, 71, -46, -102, -6, 1, 0, 4, 8, -128, 73, 161, 7, -1, 1, -4, -76, 126, 322, -164, -245, -8, 1, 1, -33, 63, 285, -295, -629, 277, 351, 9, -1, -4, 22, 121, -256, -722, 662 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Let p(n)=p(n,x) be the characteristic polynomial of the n-th principal submatrix.  The zeros of p(n) are real, and they interlace the zeros of p(n+1).  See A202605 and A204016 for guides to related sequences.

REFERENCES

(For references regarding interlacing roots, see A202605.)

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

Top of the array:

   1,  -1;

  -3,  -2,   1;

  -1,  11,   3,  -1;

   6,  -6, -29,  -4,   1;

MATHEMATICA

f[i_, j_] := Max[Floor[i/j], Floor[j/i]];

m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

TableForm[m[8]] (* 8 X 8 principal submatrix *)

Flatten[Table[f[i, n + 1 - i],

  {n, 1, 15}, {i, 1, n}]]  (* A204123 *)

p[n_] := CharacteristicPolynomial[m[n], x];

c[n_] := CoefficientList[p[n], x]

TableForm[Flatten[Table[p[n], {n, 1, 10}]]]

Table[c[n], {n, 1, 12}]

Flatten[%]                 (* A204124 *)

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

CROSSREFS

Cf. A204123, A202605, A204016.

Sequence in context: A092742 A316564 A214742 * A316674 A101479 A136170

Adjacent sequences:  A204121 A204122 A204123 * A204125 A204126 A204127

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 11 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 January 22 07:39 EST 2020. Contains 331139 sequences. (Running on oeis4.)