cp's OEIS Frontend

A204181 Symmetric matrix based on f(i,j) defined by f(i,1)=f(1,j)=1; f(i,i)= 2i-1; f(i,j)=0 otherwise; by antidiagonals.

%I A204181 #6 Mar 30 2012 18:58:08
%S A204181 1,1,1,1,3,1,1,0,0,1,1,0,5,0,1,1,0,0,0,0,1,1,0,0,7,0,0,1,1,0,0,0,0,0,
%T A204181 0,1,1,0,0,0,9,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,11,0,0,0,0,1,1,0,
%U A204181 0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,13,0,0,0,0,0,1,1,0,0,0,0,0,0
%N A204181 Symmetric matrix based on f(i,j) defined by f(i,1)=f(1,j)=1; f(i,i)= 2i-1; f(i,j)=0 otherwise; by antidiagonals.
%C A204181 A204181 represents the matrix M given by f(i,j) for i>=1 and j>=1.  See A204182 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.
%e A204181 Northwest corner:
%e A204181 1 1 1 1 1 1 1 1
%e A204181 1 3 0 0 0 0 0 0
%e A204181 1 0 5 0 0 0 0 0
%e A204181 1 0 0 7 0 0 0 0
%e A204181 1 0 0 0 9 0 0 0
%t A204181 f[i_, j_] := 0; f[1, j_] := 1;
%t A204181 f[i_, 1] := 1; f[i_, i_] := 2 i - 1;
%t A204181 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204181 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204181 Flatten[Table[f[i, n + 1 - i],
%t A204181   {n, 1, 15}, {i, 1, n}]]  (* A204181 *)
%t A204181 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204181 c[n_] := CoefficientList[p[n], x]
%t A204181 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204181 Table[c[n], {n, 1, 12}]
%t A204181 Flatten[%]                 (* A204182 *)
%t A204181 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204181 Cf. A204182, A204016, A202453.
%K A204181 nonn,tabl
%O A204181 1,5
%A A204181 _Clark Kimberling_, Jan 12 2012