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%I #8 Aug 02 2019 04:12:12
%S 2,1,1,2,3,2,1,1,1,1,2,1,4,1,2,1,3,1,1,3,1,2,1,2,5,2,1,2,1,1,1,1,1,1,
%T 1,1,2,3,4,1,6,1,4,3,2,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,7,2,1,2,1,2,1,3,
%U 1,5,3,1,1,3,5,1,3,1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,1,1,1,1,1,1,1
%N Symmetric matrix based on f(i,j) = gcd(i+1, j+1), by antidiagonals.
%C A204030 represents the matrix M given by f(i,j) = gcd(i+1, j+1) for i >= 1 and j >= 1. See A204031 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 2 1 2 1 2 1 2 1
%e 1 3 1 1 3 1 1 3
%e 2 1 4 1 2 1 4 1
%e 1 1 1 5 1 1 1 1
%e 2 3 2 1 6 1 2 3
%e 1 1 1 1 1 7 1 1
%t f[i_, j_] := GCD[i + 1, j + 1];
%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t TableForm[m[8]] (* 8 X 8 principal submatrix *)
%t Flatten[Table[f[i, n + 1 - i],
%t {n, 1, 15}, {i, 1, n}]] (* A204030 *)
%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[%] (* A204111 *)
%t TableForm[Table[c[n], {n, 1, 10}]]
%Y Cf. A204111, A204016, A202453.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Jan 11 2012
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