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A204018 Symmetric matrix based on f(i,j)=1+max{j mod i, i mod j), by antidiagonals. 3
1, 2, 2, 2, 1, 2, 2, 3, 3, 2, 2, 3, 1, 3, 2, 2, 3, 4, 4, 3, 2, 2, 3, 4, 1, 4, 3, 2, 2, 3, 4, 5, 5, 4, 3, 2, 2, 3, 4, 5, 1, 5, 4, 3, 2, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 2, 3, 4, 5, 6, 1, 6, 5, 4, 3, 2, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 2, 3, 4, 5, 6, 7, 1, 7, 6, 5, 4, 3, 2, 2, 3, 4, 5, 6, 7, 8, 8 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A204018 represents the matrix M given by f(i,j)=max{1+(j mod i), 1+( i mod j)} for i>=1 and j>=1.  See A204019 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 2 2 2

2 1 3 3 3 3

2 3 1 4 4 4

2 3 4 1 5 5

2 3 4 5 1 6

2 3 4 5 6 1

MATHEMATICA

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

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

TableForm[m[6]] (* 6x6 principal submatrix *)

Flatten[Table[f[i, n + 1 - i],

  {n, 1, 15}, {i, 1, n}]]   (* A204018 *)

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[%]                  (* A204019 *)

TableForm[Table[c[n], {n, 1, 10}]]

CROSSREFS

Cf. A204019, A204016, A202453.

Sequence in context: A106493 A083338 A241900 * A261915 A109037 A147680

Adjacent sequences:  A204015 A204016 A204017 * A204019 A204020 A204021

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 11 2012

STATUS

approved

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Last modified August 23 22:45 EDT 2019. Contains 326254 sequences. (Running on oeis4.)