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A204269 Symmetric matrix: f(i,j)=floor[(i+j+2)/4]-floor[(i+j)/4], by (constant) antidiagonals. 8
1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

A block matrix over {0,1}.  In the following guide to related matrices and permanents, Duvwxyz represents the matrix remaining after row 1 of the matrix Auvwxyz is deleted:

Matrix................Permanent of n-th submatrix

A204269=D204549.......A204422

A204545=D204269.......A204546

A204547=D204545.......A204548

A204549=D204547.......A204550

LINKS

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

EXAMPLE

Northwest corner:

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

0 0 1 1 0 0 1 1

0 1 1 0 0 1 1 0

MATHEMATICA

f[i_, j_] := Floor[(i + j + 2)/4] - Floor[(i + j)/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}]]    (* A204269 *)

Permanent[m_] :=

  With[{a = Array[x, Length[m]]},

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

Table[Permanent[m[n]], {n, 1, 22}]    (* A204422 *)

CROSSREFS

Cf. A204448, A204435.

Sequence in context: A266678 A267936 A263013 * A266216 A266300 A266605

Adjacent sequences:  A204266 A204267 A204268 * A204270 A204271 A204272

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 16 2012

STATUS

approved

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Last modified August 17 06:13 EDT 2017. Contains 290635 sequences.