

A204171


Symmetric matrix based on f(i,j)=(1 if max(i,j) is odd, and 0 otherwise), by antidiagonals.


3



1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 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, 0, 1, 0, 1, 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, 1, 0, 1, 0, 0
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OFFSET

1


COMMENTS

A204171 represents the matrix M given by f(i,j)=(1 if max(i,j) is odd, and 0 otherwise) for i>=1 and j>=1. See A204172 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:
1 0 1 0 1 0 1 0
0 0 1 0 1 0 1 0
1 1 1 0 1 0 1 0
0 0 0 0 1 0 1 0
1 1 1 1 1 0 1 0


MATHEMATICA

f[i_, j_] := If[Mod[Max[i, j], 2] == 1, 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}]] (* A204171 *)
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[%] (* A204172 *)
TableForm[Table[c[n], {n, 1, 10}]]


CROSSREFS

Cf. A204172, A204016, A202453.
Sequence in context: A266672 A266070 A262855 * A267612 A242252 A100810
Adjacent sequences: A204168 A204169 A204170 * A204172 A204173 A204174


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Jan 12 2012


STATUS

approved



