A204028 - OEIS

%I #5 Mar 30 2012 18:58:07

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

%C 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 Northwest corner:

%e 1...1...1...1....1....1

%e 1...4...4...4....4....4

%e 1...4...7...7....7....7

%e 1...4...7...10...10...10

%e 1...4...7...10...13...13

%t f[i_, j_] := Min[3 i - 2, 3 j - 2];

%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

%t TableForm[m[6]] (* 6x6 principal submatrix *)

%t Flatten[Table[f[i, n + 1 - i],

%t   {n, 1, 15}, {i, 1, n}]]  (* A204028 *)

%t p[n_] := CharacteristicPolynomial[m[n], x];

%t c[n_] := CoefficientList[p[n], x]

%t TableForm[Flatten[Table[p[n], {n, 1, 10}]]]

%t Table[c[n], {n, 1, 12}]

%t Flatten[%]                 (* A204029 *)

%t TableForm[Table[c[n], {n, 1, 10}]]

%Y Cf. A204029, A204016, A202453.

%K nonn,tabl

%O 1,5

%A _Clark Kimberling_, Jan 11 2012