A204173 Symmetric matrix based on f(i,j)=(2i-1 if max(i,j) is odd, and 0 otherwise), by antidiagonals.

1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 3, 0, 2, 0, 3, 0, 3, 0, 0, 3, 0, 4, 0, 3, 0, 3, 0, 4, 0, 4, 0, 3, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 4, 0, 5, 0, 5, 0, 4, 0, 0, 4, 0, 5, 0, 6, 0, 5, 0, 4, 0, 4, 0, 5, 0, 6, 0, 6, 0, 5, 0, 4, 4, 0, 5, 0, 6, 0, 7, 0, 6, 0, 5, 0, 4, 0, 5, 0, 6, 0, 7, 0, 7, 0, 6, 0, 5, 0, 0

Offset

1,4

Comments

A204173 represents the matrix M given by f(i,j)=(2i-1 if max(i,j) is odd, and 0 otherwise) for i>=1 and j>=1. See A204174 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 0 2 0 3 0 4 0
0 0 2 0 3 0 4 0
2 2 2 0 3 0 4 0
0 0 0 0 3 0 4 0
3 3 3 3 3 0 4 0

Mathematica

f[i_, j_] := If[Mod[Max[i, j], 2] == 1, (1 + Max[i, j])/2, 0]
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}]]  (* A204173 *)
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[%]                 (* A204174 *)
TableForm[Table[c[n], {n, 1, 10}]]

Crossrefs

Cf. A204174, A204016, A202453.

Sequence in context: A309937 A116127 A039979 * A103668 A276812 A246721

Adjacent sequences: A204170 A204171 A204172 * A204174 A204175 A204176

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 12 2012

Status

approved