A204547 - OEIS

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A204547

Symmetric matrix: f(i,j)=floor[(i+j+4)/4]-floor[(i+j+2)/4], by (constant) antidiagonals.

0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

COMMENTS

A block matrix over {0,1}. For a guide to related matrices and permanents, see A204269 and A204453.

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

Northwest corner:

0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0

1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1

0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0

1 1 0 0 1 1 0 0

1 0 0 1 1 0 0 1

MATHEMATICA

f[i_, j_] := Floor[(i + j + 4)/4] - Floor[(i + j + 2)/4];

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, 14}, {i, 1, n}]] (* A204547 *)

Permanent[m_] :=

With[{a = Array[x, Length[m]]},

Coefficient[Times @@ (m.a), Times @@ a]];

Table[Permanent[m[n]], {n, 1, 22}] (* A204548 *)

CROSSREFS

Cf. A204548, A204296.

Sequence in context: A136036 A214210 A056029 * A072609 A185012 A328794

Adjacent sequences: A204544 A204545 A204546 * A204548 A204549 A204550

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 16 2012

STATUS

approved