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A204123 Symmetric matrix based on f(i,j)=max([i/j],[j/i]), where [ ]=floor, by antidiagonals. 4
1, 2, 2, 3, 1, 3, 4, 1, 1, 4, 5, 2, 1, 2, 5, 6, 2, 1, 1, 2, 6, 7, 3, 1, 1, 1, 3, 7, 8, 3, 2, 1, 1, 2, 3, 8, 9, 4, 2, 1, 1, 1, 2, 4, 9, 10, 4, 2, 1, 1, 1, 1, 2, 4, 10, 11, 5, 3, 2, 1, 1, 1, 2, 3, 5, 11, 12, 5, 3, 2, 1, 1, 1, 1, 2, 3, 5, 12, 13, 6, 3, 2, 1, 1, 1, 1, 1, 2, 3, 6, 13, 14, 6, 4, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence represents the matrix M given by f(i,j)=max([i/j],[j/i]) for i>=1 and j>=1.  See A204124 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.

LINKS

G. C. Greubel, Table of n, a(n) for the first 100 aintidiagonals

EXAMPLE

Northwest corner:

1 2 3 4 5 6

2 1 1 2 2 3

3 1 1 1 1 2

4 2 1 1 1 1

5 2 1 1 1 1

6 3 2 1 1 1

MATHEMATICA

f[i_, j_] := Max[Floor[i/j], Floor[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}]]  (* A204123 *)

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[%]                 (* A204124 *)

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

CROSSREFS

Cf. A204124, A204016, A202453.

Sequence in context: A162911 A245327 A131821 * A237448 A204143 A143182

Adjacent sequences:  A204120 A204121 A204122 * A204124 A204125 A204126

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 11 2012

STATUS

approved

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Last modified January 19 09:08 EST 2021. Contains 340267 sequences. (Running on oeis4.)