A204431 - OEIS

%I #5 Mar 30 2012 18:58:08

%S 2,1,1,0,0,0,2,2,2,2,1,1,1,1,1,0,0,0,0,0,0,2,2,2,2,2,2,2,1,1,1,1,1,1,

%T 1,1,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,0,0,

%U 0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1

%N Symmetric matrix: f(i,j)=(2i+j+1 mod 3), by antidiagonals.

%C A block matrix over {0,1,2}.  See A204263 for a guide to related matrices and permanents.

%e Northwest corner:

%e 2 1 0 2 1 0

%e 1 0 2 1 0 2

%e 0 2 1 0 2 1

%e 2 1 0 2 1 0

%e 1 0 2 1 0 2

%e 0 2 1 0 2 1

%t f[i_, j_] := Mod[2 i + 2 j + 1, 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}]]        (* A204431 *)

%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}]   (* A204432 *)

%Y Cf. A204431, A204263.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Jan 15 2012