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A204183 Symmetric matrix based on f(i,j) defined by f(i,1)=f(1,j)=1; f(i,i)= (-1)^(i-1); f(i,j)=0 otherwise; by antidiagonals. 3
1, 1, 1, 1, -1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

A204183 represents the matrix M given by f(i,j) for i>=1 and j>=1.  See A204184 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.

LINKS

Table of n, a(n) for n=1..93.

EXAMPLE

Northwest corner:

1...1...1...1...1...1

1..-1...0...0...0...0

1...0...1...0...0...0

1...0...0..-1...0...0

1...0...0...0...1...0

MATHEMATICA

f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1;

f[i_, i_] := (-1)^(i - 1);

m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

TableForm[m[8]] (* 8x8 principal submatrix *)

Flatten[Table[f[i, n + 1 - i],

  {n, 1, 15}, {i, 1, n}]]  (* A204183 *)

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[%]                 (* A204184 *)

TableForm[Table[c[n], {n, 1, 10}]]

CROSSREFS

Cf. A204184, A204016, A202453.

Sequence in context: A014163 A308016 A166360 * A204177 A185917 A143104

Adjacent sequences:  A204180 A204181 A204182 * A204184 A204185 A204186

KEYWORD

sign,tabl

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified May 26 11:30 EDT 2022. Contains 354086 sequences. (Running on oeis4.)