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A204171 Symmetric matrix based on f(i,j)=(1 if max(i,j) is odd, and 0 otherwise), by antidiagonals. 3

%I

%S 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,

%T 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,

%U 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

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

%C 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.

%e Northwest corner:

%e 1 0 1 0 1 0 1 0

%e 0 0 1 0 1 0 1 0

%e 1 1 1 0 1 0 1 0

%e 0 0 0 0 1 0 1 0

%e 1 1 1 1 1 0 1 0

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

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

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

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

%t {n, 1, 15}, {i, 1, n}]] (* A204171 *)

%t p[n_] := CharacteristicPolynomial[m[n], x];

%t c[n_] := CoefficientList[p[n], x]

%t TableForm[Flatten[Table[p[n], {n, 1, 10}]]]

%t Table[c[n], {n, 1, 12}]

%t Flatten[%] (* A204172 *)

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

%Y Cf. A204172, A204016, A202453.

%K nonn,tabl

%O 1

%A _Clark Kimberling_, Jan 12 2012

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Last modified January 18 14:03 EST 2020. Contains 331011 sequences. (Running on oeis4.)