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A204028 Symmetric matrix based on f(i,j)=min(3i-2,3j-2), by antidiagonals.

%I A204028 #5 Mar 30 2012 18:58:07
%S A204028 1,1,1,1,4,1,1,4,4,1,1,4,7,4,1,1,4,7,7,4,1,1,4,7,10,7,4,1,1,4,7,10,10,
%T A204028 7,4,1,1,4,7,10,13,10,7,4,1,1,4,7,10,13,13,10,7,4,1,1,4,7,10,13,16,13,
%U A204028 10,7,4,1,1,4,7,10,13,16,16,13,10,7,4,1,1,4,7,10,13,16,19,16
%N A204028 Symmetric matrix based on f(i,j)=min(3i-2,3j-2), by antidiagonals.
%C A204028 A204028 represents the matrix M given by f(i,j)=min(3i-2,3j-2) for i>=1 and j>=1.  See A204029 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.
%e A204028 Northwest corner:
%e A204028 1...1...1...1....1....1
%e A204028 1...4...4...4....4....4
%e A204028 1...4...7...7....7....7
%e A204028 1...4...7...10...10...10
%e A204028 1...4...7...10...13...13
%t A204028 f[i_, j_] := Min[3 i - 2, 3 j - 2];
%t A204028 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204028 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A204028 Flatten[Table[f[i, n + 1 - i],
%t A204028   {n, 1, 15}, {i, 1, n}]]  (* A204028 *)
%t A204028 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204028 c[n_] := CoefficientList[p[n], x]
%t A204028 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204028 Table[c[n], {n, 1, 12}]
%t A204028 Flatten[%]                 (* A204029 *)
%t A204028 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204028 Cf. A204029, A204016, A202453.
%K A204028 nonn,tabl
%O A204028 1,5
%A A204028 _Clark Kimberling_, Jan 11 2012