login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 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; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

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

LINKS

Table of n, a(n) for n=1..66.

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: A130162 A175595 A175417 * A100218 A098599 A129334

Adjacent sequences:  A136478 A136479 A136480 * A136482 A136483 A136484

KEYWORD

uned,tabl,sign

AUTHOR

Roger L. Bagula, Mar 20 2008

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 July 19 03:54 EDT 2019. Contains 325144 sequences. (Running on oeis4.)