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A204006 Symmetric matrix based on f(i,j)=min{2i+j-2,i+2j-2}, 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 (list; table; graph; refs; listen; history; text; internal format)
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: A256094 A063712 A185977 * A106251 A134478 A051162

Adjacent sequences:  A204003 A204004 A204005 * A204007 A204008 A204009

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 09 2012

STATUS

approved

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Last modified October 14 03:58 EDT 2019. Contains 327995 sequences. (Running on oeis4.)