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

%I A204263 #11 Mar 06 2018 03:04:55
%S A204263 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,
%T A204263 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,
%U A204263 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
%N A204263 Symmetric matrix: f(i,j)=(i+j mod 3), by antidiagonals.
%C A204263 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:
%C A204263 Matrix................Permanent of n-th submatrix
%C A204263 A204263=D204421.......A204265
%C A204263 A204267=D204263.......A204268
%C A204263 A204421=D204267.......A179079
%C A204263 A204423=D204425.......A204424
%C A204263 A204425=D204427.......A204426
%C A204263 A204427=D204423.......A204428
%C A204263 A204429=D204431.......A204430
%C A204263 A204431=D204433.......A204432
%C A204263 A204433=D204429.......A204434
%H A204263 G. C. Greubel, <a href="/A204263/b204263.txt">Table of n, a(n) for the first 100 antidiagonals, flattened</a>
%e A204263 Northwest corner:
%e A204263 2 0 1 2 0 1
%e A204263 0 1 2 0 1 2
%e A204263 1 2 0 1 2 0
%e A204263 2 0 1 2 0 1
%e A204263 0 1 2 0 1 2
%e A204263 1 2 0 1 2 0
%t A204263 f[i_, j_] := Mod[i + j, 3];
%t A204263 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204263 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204263 Flatten[Table[f[i, n + 1 - i],
%t A204263   {n, 1, 14}, {i, 1, n}]]      (* A204263 *)
%t A204263 Permanent[m_] :=
%t A204263   With[{a = Array[x, Length[m]]},
%t A204263    Coefficient[Times @@ (m.a), Times @@ a]];
%t A204263 Table[Permanent[m[n]], {n, 1, 22}]    (* A204265 *)
%Y A204263 Cf. A204265.
%K A204263 nonn,tabl
%O A204263 1,1
%A A204263 _Clark Kimberling_, Jan 15 2012