

A204006


Symmetric matrix based on f(i,j)=min{2i+j2,i+2j2}, by antidiagonals.


3



1, 2, 2, 3, 4, 3, 4, 5, 5, 4, 5, 6, 7, 6, 5, 6, 7, 8, 8, 7, 6, 7, 8, 9, 10, 9, 8, 7, 8, 9, 10, 11, 11, 10, 9, 8, 9, 10, 11, 12, 13, 12, 11, 10, 9, 10, 11, 12, 13, 14, 14, 13, 12, 11, 10, 11, 12, 13, 14, 15, 16, 15, 14, 13, 12, 11, 12, 13, 14, 15, 16, 17, 17, 16, 15, 14, 13
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OFFSET

1,2


COMMENTS

A204006 represents the matrix M given by f(i,j)=min{2i+j,i+2j}for i>=1 and j>=1. See A204007 for characteristic polynomials of principal submatrices of M, with interlacing zeros.


LINKS

Table of n, a(n) for n=1..77.


EXAMPLE

Northwest corner:
1...2...3...4....5....6
2...4...5...6....7....8
3...5...7...8....9....10
4...6...8...10...11...12


MATHEMATICA

f[i_, j_] := Min[2 i + j  2, 2 j + i  2];
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, 12}, {i, 1, n}]] (* A204006 *)
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[%] (* A204007 *)
TableForm[Table[c[n], {n, 1, 10}]]


CROSSREFS

Cf. A204007, A202453.
Sequence in context: A063712 A340458 A185977 * A106251 A134478 A051162
Adjacent sequences: A204003 A204004 A204005 * A204007 A204008 A204009


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Jan 09 2012


STATUS

approved



