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A204160 Symmetric matrix based on f(i,j)=(3i-2 if i=j and = 0 otherwise), by antidiagonals.

%I A204160 #5 Mar 30 2012 18:58:07
%S A204160 1,1,1,1,4,1,1,1,1,1,1,1,7,1,1,1,1,1,1,1,1,1,1,1,10,1,1,1,1,1,1,1,1,1,
%T A204160 1,1,1,1,1,1,13,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,16,1,1,1,1,1,1,
%U A204160 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,19,1,1,1,1,1,1,1,1,1,1,1,1
%N A204160 Symmetric matrix based on f(i,j)=(3i-2 if i=j and = 0 otherwise), by antidiagonals.
%C A204160 A204160 represents the matrix M given by f(i,j)=(3i-2 if i=j and = 0 otherwise) for i>=1 and j>=1.  See A204161 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.
%e A204160 Northwest corner:
%e A204160 1 1 1 1
%e A204160 1 4 1 1
%e A204160 1 1 7 1
%e A204160 1 1 1 10
%t A204160 f[i_, j_] := 1; f[i_, i_] := 3 i - 2;
%t A204160 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204160 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204160 Flatten[Table[f[i, n + 1 - i],
%t A204160   {n, 1, 15}, {i, 1, n}]]    (* A204160 *)
%t A204160 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204160 c[n_] := CoefficientList[p[n], x]
%t A204160 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204160 Table[c[n], {n, 1, 12}]
%t A204160 Flatten[%]                   (* A204161 *)
%t A204160 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204160 Cf. A204161, A204016, A202453.
%K A204160 nonn,tabl
%O A204160 1,5
%A A204160 _Clark Kimberling_, Jan 12 2012