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A204175 Symmetric matrix based on f(i,j)=(1 if max(i,j) is even, and 0 otherwise), by antidiagonals. 2
0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

A204175 represents the matrix M given by f(i,j)=(1 if max(i,j) is even, and 0 otherwise) for i>=1 and j>=1.  See A204176 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..99.

EXAMPLE

Northwest corner:

0 1 0 1 0 1 0 1

1 1 0 1 0 1 0 1

0 0 0 1 0 1 0 1

1 1 1 1 0 1 0 1

0 0 0 0 0 1 0 1

1 1 1 1 1 1 0 1

MATHEMATICA

f[i_, j_] := If[Mod[Max[i, j], 2] == 0, 1, 0]

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}]]  (* A204175 *)

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[%]                 (* A204176 *)

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

CROSSREFS

Cf. A204176, A204016, A202453.

Sequence in context: A131929 A100821 A139689 * A285255 A324823 A284912

Adjacent sequences:  A204172 A204173 A204174 * A204176 A204177 A204178

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified November 14 01:24 EST 2019. Contains 329108 sequences. (Running on oeis4.)