cp's OEIS Frontend

A204166 Symmetric matrix based on f(i,j)=ceiling[(i+j)/2], by antidiagonals.

%I A204166 #5 Mar 30 2012 18:58:07
%S A204166 1,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,
%T A204166 5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,
%U A204166 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8
%N A204166 Symmetric matrix based on f(i,j)=ceiling[(i+j)/2], by antidiagonals.
%C A204166 A204166 represents the matrix M given by f(i,j)=ceiling[(i+j)/2] for i>=1 and j>=1.  See A204167 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.
%e A204166 Northwest corner:
%e A204166 1 2 2 3 3 4 4 5
%e A204166 2 2 3 3 4 4 5 5
%e A204166 2 3 3 4 4 5 5 6
%e A204166 3 3 4 4 5 5 6 6
%t A204166 f[i_, j_] := Ceiling[(i + j)/2];
%t A204166 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204166 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204166 Flatten[Table[f[i, n + 1 - i],
%t A204166   {n, 1, 15}, {i, 1, n}]]  (* A204166 *)
%t A204166 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204166 c[n_] := CoefficientList[p[n], x]
%t A204166 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204166 Table[c[n], {n, 1, 12}]
%t A204166 Flatten[%]                 (* A204167 *)
%t A204166 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204166 Cf. A204167, A204016, A202453.
%K A204166 nonn,tabl
%O A204166 1,2
%A A204166 _Clark Kimberling_, Jan 12 2012