

A204022


Symmetric matrix based on f(i,j)=max(2i1, 2j1), 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
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OFFSET

1,2


COMMENTS

A204022 represents the matrix M given by f(i,j)=max(2i1,2j1) 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 A255316 A078587
Adjacent sequences: A204019 A204020 A204021 * A204023 A204024 A204025


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Jan 11 2012


STATUS

approved



