A204177 Symmetric matrix based on f(i,j)=(1 if i=1 or j=1 or i=j, and 0 otherwise), by antidiagonals.

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, 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, 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

Offset

1

Comments

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.

Links

Table of n, a(n) for n=1..99.

Example

Northwest corner:
1 1 1 1 1 1 1 1
1 1 0 0 0 0 0 0
1 0 1 0 0 0 0 0
1 0 0 1 0 0 0 0
1 0 0 0 1 0 0 0
1 0 0 0 0 1 0 0

Mathematica

f[i_, j_] := 0; f[1, j_] := 1;
 f[i_, 1] := 1; f[i_, i_] := 1;
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 15}, {i, 1, n}]]  (* A204177 *)
p[n_] := CharacteristicPolynomial[m[n], x];
c[n_] := CoefficientList[p[n], x]
TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
Table[c[n], {n, 1, 12}]
Flatten[%]                 (* A204178 *)
TableForm[Table[c[n], {n, 1, 10}]]

Crossrefs

Cf. A204178, A204016, A202453.

Sequence in context: A308016 A166360 A204183 * A185917 A143104 A127236

Adjacent sequences: A204174 A204175 A204176 * A204178 A204179 A204180

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 12 2012

Status

approved