A204177 - OEIS

%I #5 Mar 30 2012 18:58:08

%S 1,1,1,1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0,0,0,0,

%T 0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,1,1,0,

%U 0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0

%N Symmetric matrix based on f(i,j)=(1 if i=1 or j=1 or i=j, and 0 otherwise), by antidiagonals.

%C A204177 represents the matrix M given by f(i,j)=(1 if i=1 or j=1 or i=j, and 0 otherwise) for i>=1 and j>=1.  See A204178 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.  A185917 is a signed variant of A204177.

%e Northwest corner:

%e 1 1 1 1 1 1 1 1

%e 1 1 0 0 0 0 0 0

%e 1 0 1 0 0 0 0 0

%e 1 0 0 1 0 0 0 0

%e 1 0 0 0 1 0 0 0

%e 1 0 0 0 0 1 0 0

%t f[i_, j_] := 0; f[1, j_] := 1;

%t  f[i_, 1] := 1; f[i_, i_] := 1;

%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

%t TableForm[m[8]] (* 8x8 principal submatrix *)

%t Flatten[Table[f[i, n + 1 - i],

%t   {n, 1, 15}, {i, 1, n}]]  (* A204177 *)

%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[%]                 (* A204178 *)

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

%Y Cf. A204178, A204016, A202453.

%K nonn,tabl

%O 1

%A _Clark Kimberling_, Jan 12 2012