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A204012 Symmetric matrix based on f(i,j)=min{3i+j-3,i+3j-3}, by antidiagonals.

%I A204012 #5 Mar 30 2012 18:58:07
%S A204012 1,2,2,3,5,3,4,6,6,4,5,7,9,7,5,6,8,10,10,8,6,7,9,11,13,11,9,7,8,10,12,
%T A204012 14,14,12,10,8,9,11,13,15,17,15,13,11,9,10,12,14,16,18,18,16,14,12,10,
%U A204012 11,13,15,17,19,21,19,17,15,13,11,12,14,16,18,20,22,22,20,18
%N A204012 Symmetric matrix based on f(i,j)=min{3i+j-3,i+3j-3}, by antidiagonals.
%C A204012 A204012 represents the matrix M given by f(i,j)=max{3i+j-3,i+3j-3}for i>=1 and j>=1.  See A204013 for characteristic polynomials of principal submatrices of M, with interlacing zeros.
%e A204012 Northwest corner:
%e A204012 1....2....3....4....5....6
%e A204012 2....5....6....7....8....9
%e A204012 3....6....9....10...11...12
%e A204012 4....7....10...13...14...15
%t A204012 f[i_, j_] := Min[3 i + j - 3, 3 j + i - 3];
%t A204012 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204012 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A204012 Flatten[Table[f[i, n + 1 - i],
%t A204012 {n, 1, 12}, {i, 1, n}]]   (* A204012 *)
%t A204012 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204012 c[n_] := CoefficientList[p[n], x]
%t A204012 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204012 Table[c[n], {n, 1, 12}]
%t A204012 Flatten[%]  (* A204013 *)
%t A204012 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204012 Cf. A204013, A202453.
%K A204012 nonn,tabl
%O A204012 1,2
%A A204012 _Clark Kimberling_, Jan 10 2012