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A204022 Symmetric matrix based on f(i,j)=max(2i-1, 2j-1), by antidiagonals. 3
1, 3, 3, 5, 3, 5, 7, 5, 5, 7, 9, 7, 5, 7, 9, 11, 9, 7, 7, 9, 11, 13, 11, 9, 7, 9, 11, 13, 15, 13, 11, 9, 9, 11, 13, 15, 17, 15, 13, 11, 9, 11, 13, 15, 17, 19, 17, 15, 13, 11, 11, 13, 15, 17, 19, 21, 19, 17, 15, 13, 11, 13, 15, 17, 19, 21, 23, 21, 19, 17, 15, 13, 13, 15, 17 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A204022 represents the matrix M given by f(i,j)=max(2i-1,2j-1) for i>=1 and j>=1.  See A204023 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..75.

EXAMPLE

Northwest corner:

1 3 5 7 9

3 3 5 7 9

5 5 5 7 9

7 7 7 7 9

9 9 9 9 9

MATHEMATICA

f[i_, j_] := Max[2 i - 1, 2 j - 1];

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}]]          (* A204022 *)

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[%]                         (* A204023 *)

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

CROSSREFS

Cf. A204022, A204016, A202453.

Sequence in context: A158894 A131919 A185154 * A131832 A078587 A239931

Adjacent sequences:  A204019 A204020 A204021 * A204023 A204024 A204025

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 11 2012

STATUS

approved

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Last modified April 17 03:52 EDT 2014. Contains 240628 sequences.