A204263 - OEIS

%I #11 Mar 06 2018 03:04:55

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

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

%C A204263=D204421.......A204265

%C A204267=D204263.......A204268

%C A204421=D204267.......A179079

%C A204423=D204425.......A204424

%C A204425=D204427.......A204426

%C A204427=D204423.......A204428

%C A204429=D204431.......A204430

%C A204431=D204433.......A204432

%C A204433=D204429.......A204434

%H G. C. Greubel, <a href="/A204263/b204263.txt">Table of n, a(n) for the first 100 antidiagonals, flattened</a>

%e Northwest corner:

%e 2 0 1 2 0 1

%e 0 1 2 0 1 2

%e 1 2 0 1 2 0

%e 2 0 1 2 0 1

%e 0 1 2 0 1 2

%e 1 2 0 1 2 0

%t f[i_, j_] := Mod[i + j, 3];

%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

%t TableForm[m[8]] (* 8x8 principal submatrix *)

%t Flatten[Table[f[i, n + 1 - i],

%t   {n, 1, 14}, {i, 1, n}]]      (* A204263 *)

%t Permanent[m_] :=

%t   With[{a = Array[x, Length[m]]},

%t    Coefficient[Times @@ (m.a), Times @@ a]];

%t Table[Permanent[m[n]], {n, 1, 22}]    (* A204265 *)

%Y Cf. A204265.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Jan 15 2012