A204006 - OEIS

%I #13 Feb 06 2023 14:03:33

%S 1,2,2,3,4,3,4,5,5,4,5,6,7,6,5,6,7,8,8,7,6,7,8,9,10,9,8,7,8,9,10,11,

%T 11,10,9,8,9,10,11,12,13,12,11,10,9,10,11,12,13,14,14,13,12,11,10,11,

%U 12,13,14,15,16,15,14,13,12,11,12,13,14,15,16,17,17,16,15,14,13,12

%N Symmetric matrix based on f(i,j) = min{2i+j-2,i+2j-2}, by antidiagonals.

%C A204006 represents the matrix M given by f(i,j) = min{2i+j,i+2j} for i>=1 and j>=1.  See A204007 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

%e Northwest corner:

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

%e 2...4...5...6....7....8

%e 3...5...7...8....9....10

%e 4...6...8...10...11...12

%t f[i_, j_] := Min[2 i + j - 2, 2 j + i - 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, 12}, {i, 1, n}]]   (* A204006 *)

%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[%]                (* A204007 *)

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

%Y Cf. A204007, A202453.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Jan 09 2012