A204166 - OEIS

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A204166

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

1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, 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, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

A204166 represents the matrix M given by f(i,j)=ceiling[(i+j)/2] for i>=1 and j>=1. See A204167 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 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_] := Ceiling[(i + j)/2];

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

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