A204156 - OEIS

A204156

Symmetric matrix based on f(i,j)=max(3i-j, 3j-i), by antidiagonals.

1, 4, 4, 7, 3, 7, 10, 6, 6, 10, 13, 9, 5, 9, 13, 16, 12, 8, 8, 12, 16, 19, 15, 11, 7, 11, 15, 19, 22, 18, 14, 10, 10, 14, 18, 22, 25, 21, 17, 13, 9, 13, 17, 21, 25, 28, 24, 20, 16, 12, 12, 16, 20, 24, 28, 31, 27, 23, 19, 15, 11, 15, 19, 23, 27, 31, 34, 30, 26, 22, 18

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OFFSET

1,2

COMMENTS

A204156 represents the matrix M given by f(i,j)=max(3i-j, 3j-i) for i>=1 and j>=1. See A204157 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..71.

EXAMPLE

Northwest corner:

1...4...7...10..13

4...3...6...9...12

7...6...5...8...11

10..9...8...7...10

MATHEMATICA

f[i_, j_] := -1 + Max[3 i - j, 3 j - i];

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

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