A204125 Symmetric matrix based on f(i,j)=(i if i=j and 1 otherwise), by antidiagonals.

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,5

Comments

A204125 represents the matrix M given by f(i,j)=max([i/j],[j/i]) for i>=1 and j>=1. See A204126 for characteristic polynomials of principal submatrices of M, with interlacing zeros. See A204016 for a guide to other choices of M.

Links

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

Example

Northwest corner:
1 1 1 1 1 1
1 2 1 1 1 1
1 1 3 1 1 1
1 1 1 4 1 1
1 1 1 1 5 1
1 1 1 1 1 6

Mathematica

f[i_, j_] := 1; f[i_, i_] := i;
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}]]  (* A204125 *)
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[%]                 (* A204126 *)
TableForm[Table[c[n], {n, 1, 10}]]

Crossrefs

Cf. A204126, A204016, A202453.

Sequence in context: A081387 A261795 A306345 * A204127 A225174 A059895

Adjacent sequences: A204122 A204123 A204124 * A204126 A204127 A204128

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 11 2012

Status

approved