login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A204111 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j) = gcd(i+1, j+1) (A204030). 3
2, -1, 5, -5, 1, 10, -20, 9, -1, 44, -100, 62, -14, 1, 104, -328, 330, -128, 20, -1, 656, -2208, 2476, -1176, 263, -27, 1, 2624, -10144, 13992, -8880, 2804, -452, 35, -1, 15744, -66112, 102384, -75760, 29512, -6336, 744, -44, 1, 67584 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
EXAMPLE
Top of the array:
2, -1;
5, -5, 1;
10, -20, 9, -1;
44, -100, 62, -14, 1;
MATHEMATICA
f[i_, j_] := GCD[i + 1, j + 1];
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}]] (* A204030 *)
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[%] (* A204111 *)
TableForm[Table[c[n], {n, 1, 10}]]
CROSSREFS
Sequence in context: A209695 A033282 A126350 * A079502 A209164 A209148
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 29 18:12 EST 2024. Contains 370428 sequences. (Running on oeis4.)