A204000 - OEIS

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

%S 1,2,2,3,5,3,4,7,7,4,5,9,11,9,5,6,11,14,14,11,6,7,13,17,19,17,13,7,8,

%T 15,20,23,23,20,15,8,9,17,23,27,29,27,23,17,9,10,19,26,31,34,34,31,26,

%U 19,10,11,21,29,35,39,41,39,35,29,21,11,12,23,32,39,44,47,47

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

%C A204000 represents the matrix M given by f(i,j)=min{i(j+1)-1,j(i+1)-1}for i>=1 and j>=1.  See A204001 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

%e Northwest corner:

%e 1...2....3....4....5....6

%e 2...5....7....9....11...13

%e 3...7....11...14...17...20

%e 4...9....14...19...23...27

%e 5...11...17...23...29...34

%t f[i_, j_] := Min[i (j + 1) - 1, j (i + 1) - 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}]]    (* A204000 *)

%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[%]              (* A204001 *)

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

%Y Cf. A204001, A202453.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Jan 09 2012