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A204158 Symmetric matrix based on f(i,j)=max(3i-2j, 3j-2i), by antidiagonals.

%I A204158 #5 Mar 30 2012 18:58:07
%S A204158 1,4,4,7,2,7,10,5,5,10,13,8,3,8,13,16,11,6,6,11,16,19,14,9,4,9,14,19,
%T A204158 22,17,12,7,7,12,17,22,25,20,15,10,5,10,15,20,25,28,23,18,13,8,8,13,
%U A204158 18,23,28,31,26,21,16,11,6,11,16,21,26,31,34,29,24,19,14,9,9,14
%N A204158 Symmetric matrix based on f(i,j)=max(3i-2j, 3j-2i), by antidiagonals.
%C A204158 A204158 represents the matrix M given by f(i,j)=max(3i-2j, 3j-2i) for i>=1 and j>=1.  See A204159 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.
%e A204158 Northwest corner:
%e A204158 1....4....7....10...13
%e A204158 4....2....5....8....11
%e A204158 7....5....3....6....9
%e A204158 10...8....6....4....7
%t A204158 f[i_, j_] := Max[3 i - 2 j, 3 j - 2 i];
%t A204158 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204158 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204158 Flatten[Table[f[i, n + 1 - i],
%t A204158   {n, 1, 15}, {i, 1, n}]]   (* A204158 *)
%t A204158 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204158 c[n_] := CoefficientList[p[n], x]
%t A204158 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204158 Table[c[n], {n, 1, 12}]
%t A204158 Flatten[%]                  (* A204159 *)
%t A204158 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204158 Cf. A204159, A204016, A202453.
%K A204158 nonn,tabl
%O A204158 1,2
%A A204158 _Clark Kimberling_, Jan 12 2012