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A204158 Symmetric matrix based on f(i,j)=max(3i-2j, 3j-2i), by antidiagonals. 5
1, 4, 4, 7, 2, 7, 10, 5, 5, 10, 13, 8, 3, 8, 13, 16, 11, 6, 6, 11, 16, 19, 14, 9, 4, 9, 14, 19, 22, 17, 12, 7, 7, 12, 17, 22, 25, 20, 15, 10, 5, 10, 15, 20, 25, 28, 23, 18, 13, 8, 8, 13, 18, 23, 28, 31, 26, 21, 16, 11, 6, 11, 16, 21, 26, 31, 34, 29, 24, 19, 14, 9, 9, 14 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A204158 represents the matrix M given by f(i,j)=max(3i-2j, 3j-2i) for i>=1 and j>=1.  See A204159 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..74.

EXAMPLE

Northwest corner:

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

4....2....5....8....11

7....5....3....6....9

10...8....6....4....7

MATHEMATICA

f[i_, j_] := Max[3 i - 2 j, 3 j - 2 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}]]   (* A204158 *)

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[%]                  (* A204159 *)

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

CROSSREFS

Cf. A204159, A204016, A202453.

Sequence in context: A131844 A010476 A020762 * A053510 A197009 A204156

Adjacent sequences:  A204155 A204156 A204157 * A204159 A204160 A204161

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)