A204164 Symmetric matrix based on f(i,j)=floor[(i+j)/2], by antidiagonals.

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

Offset

1,4

Comments

A204164 represents the matrix M given by f(i,j)=floor[(i+j)/2] for i>=1 and j>=1. See A204165 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 2 2 3 3 4 4
1 2 2 3 3 4 4 5
2 2 3 3 4 4 5 5
2 3 3 4 4 5 5 6
3 3 4 4 5 5 6 6

Mathematica

f[i_, j_] := Floor[(i + j)/2];
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}]]  (* A204164 *)
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[%]                 (* A204165 *)
TableForm[Table[c[n], {n, 1, 10}]]

Crossrefs

Cf. A204165, A204016, A202453.

Sequence in context: A076080 A134914 A329195 * A257639 A180447 A295866

Adjacent sequences: A204161 A204162 A204163 * A204165 A204166 A204167

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 12 2012

Status

approved