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!)
A204011 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max{3i+j-3,i+3j-3} (A204008). 3
1, -1, -11, -6, 1, 40, 70, 15, -1, -116, -328, -240, -28, 1, 304, 1176, 1456, 610, 45, -1, -752, -3680, -6408, -4704, -1295, -66, 1, 1792, 10592, 23760, 25080, 12432, 2436, 91, -1, -4160, -28800, -79040 (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 for a guide to related sequences.
REFERENCES
(For references regarding interlacing roots, see A202605.)
LINKS
EXAMPLE
Top of the array:
1.....-1
-11....-6.....1
40.....70....15....-1
-116...-328..-240....1
MATHEMATICA
f[i_, j_] := Max[3 i + j - 3, 3 j + i - 3];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[6]] (* 6x6 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
{n, 1, 12}, {i, 1, n}]] (* A204008 *)
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[%] (* A204011 *)
TableForm[Table[c[n], {n, 1, 10}]]
CROSSREFS
Sequence in context: A348063 A090840 A227775 * A359439 A359492 A347357
KEYWORD
tabl,sign
AUTHOR
Clark Kimberling, Jan 09 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 March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)