|
Search: id:A136481
|
|
|
| A136481 |
|
Symmetric polynomial matrices that give multivariate determinants as Coefficients of characteristic polynomials: h(n,m)=If[m == 1, n, If[n - m + 1 == 0, 1, If[n - m == 0, 1, If[n - m > 0, 1, 0]]]],n,m<=d. |
|
+0
1
|
|
| 1, 1, -1, -1, -2, 1, 1, 0, 3, -1, -1, 0, 2, -4, 1, 1, 0, 0, -5, 5, -1, -1, 0, 0, -2, 9, -6, 1, 1, 0, 0, 0, 7, -14, 7, -1, -1, 0, 0, 0, 2, -16, 20, -8, 1, 1, 0, 0, 0, 0, -9, 30, -27, 9, -1, -1, 0, 0, 0, 0, -2, 25, -50, 35, -10, 1
(list; table; graph; listen)
|
|
|
OFFSET
|
1,5
|
|
|
COMMENT
|
Row sums are:
{1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2}
|
|
REFERENCES
|
Terr, David and Weisstein, Eric W. "Symmetric Polynomial." http : // mathworld.wolfram.com/SymmetricPolynomial.html
|
|
FORMULA
|
h(n,m)=If[m == 1, n, If[n - m + 1 == 0, 1, If[n - m == 0, 1, If[n - m > 0, 1, 0]]]],n,m<=d
|
|
EXAMPLE
|
{1},
{1, -1},
{-1, -2, 1},
{1, 0, 3, -1},
{-1, 0, 2, -4, 1},
{1, 0, 0, -5, 5, -1},
{-1, 0, 0, -2, 9, -6, 1},
{1, 0, 0, 0, 7, -14, 7, -1},
{-1,0, 0, 0, 2, -16, 20, -8, 1},
{1, 0, 0, 0, 0, -9, 30, -27,9, -1},
{-1, 0, 0, 0, 0, -2, 25, -50, 35, -10, 1}
|
|
MATHEMATICA
|
f[n_, m_] := If[m == 1, n, If[n - m + 1 == 0, 1, If[n - m == 0, 1, If[n - m > 0, 1, 0]]]]; M[d_] := Table[Table[f[n, m], {n, 1, d}], {m, 1, d}]; a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[M[n], x], x], {n, 1, 10}]]; Flatten[a]
|
|
CROSSREFS
|
Cf. A100218, A098599.
Sequence in context: A128589 A130162 A133736 this_sequence A100218 A098599 A129334
Adjacent sequences: A136478 A136479 A136480 this_sequence A136482 A136483 A136484
|
|
KEYWORD
|
uned,tabl,sign
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 20 2008
|
|
|
Search completed in 0.002 seconds
|
