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A204173 Symmetric matrix based on f(i,j)=(2i-1 if max(i,j) is odd, and 0 otherwise), by antidiagonals. 2
1, 0, 0, 2, 0, 2, 0, 2, 2, 0, 3, 0, 2, 0, 3, 0, 3, 0, 0, 3, 0, 4, 0, 3, 0, 3, 0, 4, 0, 4, 0, 3, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 4, 0, 5, 0, 5, 0, 4, 0, 0, 4, 0, 5, 0, 6, 0, 5, 0, 4, 0, 4, 0, 5, 0, 6, 0, 6, 0, 5, 0, 4, 4, 0, 5, 0, 6, 0, 7, 0, 6, 0, 5, 0, 4, 0, 5, 0, 6, 0, 7, 0, 7, 0, 6, 0, 5, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A204173 represents the matrix M given by f(i,j)=(2i-1 if max(i,j) is odd, and 0 otherwise) for i>=1 and j>=1.  See A204174 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..99.

EXAMPLE

Northwest corner:

1 0 2 0 3 0 4 0

0 0 2 0 3 0 4 0

2 2 2 0 3 0 4 0

0 0 0 0 3 0 4 0

3 3 3 3 3 0 4 0

MATHEMATICA

f[i_, j_] := If[Mod[Max[i, j], 2] == 1, (1 + Max[i, j])/2, 0]

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}]]  (* A204173 *)

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[%]                 (* A204174 *)

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

CROSSREFS

Cf. A204174, A204016, A202453.

Sequence in context: A309937 A116127 A039979 * A103668 A276812 A246721

Adjacent sequences:  A204170 A204171 A204172 * A204174 A204175 A204176

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified January 28 07:04 EST 2020. Contains 331317 sequences. (Running on oeis4.)