A204267 -id:A204267 - cp's OEIS frontend

A204268 Permanent of the n-th principal submatrix of A204267.

0, 1, 9, 16, 132, 1032, 5184, 51912, 530712, 4188672, 53529984, 707802624, 7614259200, 119716185600, 1938416832000, 26579819520000, 496487584512000, 9509523337728000, 158654296829952000, 3434389946233344000

Offset: 1

Clark Kimberling, Jan 15 2012

nonn

G. C. Greubel, Table of n, a(n) for n = 1..100

Cf. A204267.

f[i_, j_] := Mod[i + j + 1, 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}]]    (* A204267 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 22}]  (* A204268 *)

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

Original entry on oeis.org

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

Clark Kimberling, Jan 15 2012

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

			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

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

Cf. A204265.

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 *)

cp's OEIS Frontend

A204268 Permanent of the n-th principal submatrix of A204267.

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