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A204263
Symmetric matrix: f(i,j)=(i+j mod 3), by antidiagonals.
22
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
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 15 2012
STATUS
approved