A204435 Symmetric matrix: f(i,j)=((i+j)^2 mod 3), read by (constant) antidiagonals.

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

Offset

1

Comments

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

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

A204435=D204439.....A204436

A204437=D204435.....A204438

A204439=D204437.....A204439

A204441=D204447.....A204442

A204443=D204441.....A204444

A204445=D204443.....A204446

A204447=D204445.....A204448

Homer and Goldman mention this as an example of a two-dimensional recurrence. - N. J. A. Sloane, Aug 29 2018

References

Homer, Steven, and Jerry Goldman. "Doubly-periodic sequences and two-dimensional recurrences." SIAM Journal on Algebraic Discrete Methods 6.3 (1985): 360-370. See page 369.

Links

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

Example

Northwest corner:
1 0 1 1 0 1
0 1 1 0 1 1
1 1 0 1 1 0
1 0 1 1 0 1
0 1 1 0 1 1
1 1 0 1 1 0

Mathematica

f[i_, j_] := Mod[(i + j)^2, 3];
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}]]       (* A204435 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 22}]   (* A204436 *)

Crossrefs

Cf. A204436.

Sequence in context: A194661 A285427 A285621 * A331313 A267155 A204445

Adjacent sequences: A204432 A204433 A204434 * A204436 A204437 A204438

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 15 2012

Status

approved