|
Search: id:A136458
|
|
|
| A136458 |
|
Triangle of coefficients of the characteristic polynomial of an bi-orthogonnal nXn matrix: h(i,j)=If[i - j == 0, 1, If[Abs[i - j] - n/2 == 0, -1, 0]];i,j<=n; example n=4: {{1, 0, -1, 0}, {0, 1, 0, -1}, {-1, 0, 1, 0}, {0, -1, 0, 1}}. |
|
+0
1
|
|
| 1, 1, -1, 0, -2, 1, 1, -3, 3, -1, 0, 0, 4, -4, 1, 1, -5, 10, -10, 5, -1, 0, 0, 0, -8, 12, -6, 1, 1, -7, 21, -35, 35, -21, 7, -1, 0, 0, 0, 0, 16, -32, 24, -8, 1, 1, -9, 36, -84, 126, -126, 84, -36, 9, -1, 0, 0, 0, 0, 0, -32, 80, -80, 40, -10, 1
(list; table; graph; listen)
|
|
|
OFFSET
|
1,5
|
|
|
COMMENT
|
Row sums are:
{1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1}
These matrices are related to binary digital signal processing.
|
|
REFERENCES
|
http://www.ee.cityu.edu.hk/~eekwwong/ee40214/chapter3.pdf
|
|
FORMULA
|
If[i - j == 0, 1, If[Abs[i - j] - n/2 == 0, -1, 0]],
|
|
EXAMPLE
|
{1},
{1, -1},
{0, -2, 1},
{1, -3, 3, -1},
{0, 0, 4, -4, 1},
{1, -5, 10, -10, 5, -1},
{0, 0, 0, -8, 12, -6, 1},
{1, -7, 21, -35, 35, -21, 7, -1},
{0, 0, 0, 0, 16, -32, 24, -8, 1},
{1, -9, 36, -84, 126, -126, 84, -36, 9, -1},
{0, 0, 0, 0, 0, -32, 80, -80, 40, -10, 1}
|
|
MATHEMATICA
|
Clear[B] B[n_] := Table[Table[If[i -j == 0, 1, If[Abs[i - j] - n/2 == 0, -1, 0]], {i, 1, n}], {j, 1, n}]; a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[B[n], x], x], {n, 1, 10}]]; Flatten[a] Join[{1}, Table[Apply[Plus, CoefficientList[CharacteristicPolynomial[B[n], x], x]], {n, 1, 10}]];
|
|
CROSSREFS
|
Sequence in context: A078802 A108482 A124750 this_sequence A048805 A129571 A034931
Adjacent sequences: A136455 A136456 A136457 this_sequence A136459 A136460 A136461
|
|
KEYWORD
|
uned,tabl,sign
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 20 2008
|
|
|
Search completed in 0.002 seconds
|
