A203996 - OEIS

%I #12 Jul 08 2024 11:11:27

%S 2,3,3,4,6,4,5,8,8,5,6,10,12,10,6,7,12,15,15,12,7,8,14,18,20,18,14,8,

%T 9,16,21,24,24,21,16,9,10,18,24,28,30,28,24,18,10,11,20,27,32,35,35,

%U 32,27,20,11,12,22,30,36,40,42,40,36,30,22,12,13,24,33,40,45,48

%N Symmetric matrix based on f(i,j)=min{i(j+1),j(i+1)}, by antidiagonals.

%C A203996 represents the matrix M given by f(i,j)=min{i(j+1),j(i+1)} for i>=1 and j>=1.  See A203997 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

%e Northwest corner:

%e 2...3....4....5....6....7

%e 3...6....8....10...12...14

%e 4...8....12...15...18...21

%e 5...10...15...20...24...28

%t f[i_, j_] := Min[i (j + 1), j (i + 1)];

%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, 12}, {i, 1, n}]]   (* A203996 *)

%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[%]      (* A203997 *)

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

%Y Cf. A203995, A202453.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Jan 09 2012