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A204156 Symmetric matrix based on f(i,j)=max(3i-j, 3j-i), by antidiagonals.

%I A204156 #5 Mar 30 2012 18:58:07
%S A204156 1,4,4,7,3,7,10,6,6,10,13,9,5,9,13,16,12,8,8,12,16,19,15,11,7,11,15,
%T A204156 19,22,18,14,10,10,14,18,22,25,21,17,13,9,13,17,21,25,28,24,20,16,12,
%U A204156 12,16,20,24,28,31,27,23,19,15,11,15,19,23,27,31,34,30,26,22,18
%N A204156 Symmetric matrix based on f(i,j)=max(3i-j, 3j-i), by antidiagonals.
%C A204156 A204156 represents the matrix M given by f(i,j)=max(3i-j, 3j-i) for i>=1 and j>=1.  See A204157 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.
%e A204156 Northwest corner:
%e A204156 1...4...7...10..13
%e A204156 4...3...6...9...12
%e A204156 7...6...5...8...11
%e A204156 10..9...8...7...10
%t A204156 f[i_, j_] := -1 + Max[3 i - j, 3 j - i];
%t A204156 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204156 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204156 Flatten[Table[f[i, n + 1 - i],
%t A204156   {n, 1, 15}, {i, 1, n}]]    (* A204156 *)
%t A204156 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204156 c[n_] := CoefficientList[p[n], x]
%t A204156 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204156 Table[c[n], {n, 1, 12}]
%t A204156 Flatten[%]                   (* A204157 *)
%t A204156 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204156 Cf. A204157, A204016, A202453.
%K A204156 nonn,tabl
%O A204156 1,2
%A A204156 _Clark Kimberling_, Jan 12 2012