A204263 Symmetric matrix: f(i,j)=(i+j mod 3), by antidiagonals.

2, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,1

Comments

A block matrix over {0,1,2}. 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

A204263=D204421.......A204265

A204267=D204263.......A204268

A204421=D204267.......A179079

A204423=D204425.......A204424

A204425=D204427.......A204426

A204427=D204423.......A204428

A204429=D204431.......A204430

A204431=D204433.......A204432

A204433=D204429.......A204434

Links

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

Example

Northwest corner:
2 0 1 2 0 1
0 1 2 0 1 2
1 2 0 1 2 0
2 0 1 2 0 1
0 1 2 0 1 2
1 2 0 1 2 0

Mathematica

f[i_, j_] := Mod[i + j, 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}]]      (* A204263 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 22}]    (* A204265 *)

Crossrefs

Cf. A204265.

Sequence in context: A124764 A151899 A268374 * A228347 A209314 A079632

Adjacent sequences: A204260 A204261 A204262 * A204264 A204265 A204266

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 15 2012

Status

approved