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A204156 Symmetric matrix based on f(i,j)=max(3i-j, 3j-i), by antidiagonals. 3
1, 4, 4, 7, 3, 7, 10, 6, 6, 10, 13, 9, 5, 9, 13, 16, 12, 8, 8, 12, 16, 19, 15, 11, 7, 11, 15, 19, 22, 18, 14, 10, 10, 14, 18, 22, 25, 21, 17, 13, 9, 13, 17, 21, 25, 28, 24, 20, 16, 12, 12, 16, 20, 24, 28, 31, 27, 23, 19, 15, 11, 15, 19, 23, 27, 31, 34, 30, 26, 22, 18 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A204156 represents the matrix M given by f(i,j)=max(3i-j, 3j-i) for i>=1 and j>=1.  See A204157 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..71.

EXAMPLE

Northwest corner:

1...4...7...10..13

4...3...6...9...12

7...6...5...8...11

10..9...8...7...10

MATHEMATICA

f[i_, j_] := -1 + Max[3 i - j, 3 j - i];

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

TableForm[m[8]] (* 8x8 principal submatrix *)

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

  {n, 1, 15}, {i, 1, n}]]    (* A204156 *)

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[%]                   (* A204157 *)

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

CROSSREFS

Cf. A204157, A204016, A202453.

Sequence in context: A204158 A053510 A197009 * A163106 A258972 A146564

Adjacent sequences:  A204153 A204154 A204155 * A204157 A204158 A204159

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified March 20 09:35 EDT 2019. Contains 321345 sequences. (Running on oeis4.)