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%I #10 Aug 29 2018 01:19:01
%S 1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,
%T 0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0
%N Symmetric matrix: f(i,j)=((i+j)^2 mod 3), read by (constant) antidiagonals.
%C A block matrix over {0,1}. In the following guide to related matrices and permanents, Duvwxyz means the matrix remaining after deleting row 1 of the matrix Auvwxyz:
%C Matrix..............Permanent of n-th submatrix
%C A204435=D204439.....A204436
%C A204437=D204435.....A204438
%C A204439=D204437.....A204439
%C A204441=D204447.....A204442
%C A204443=D204441.....A204444
%C A204445=D204443.....A204446
%C A204447=D204445.....A204448
%C Homer and Goldman mention this as an example of a two-dimensional recurrence. - _N. J. A. Sloane_, Aug 29 2018
%D Homer, Steven, and Jerry Goldman. "Doubly-periodic sequences and two-dimensional recurrences." SIAM Journal on Algebraic Discrete Methods 6.3 (1985): 360-370. See page 369.
%e Northwest corner:
%e 1 0 1 1 0 1
%e 0 1 1 0 1 1
%e 1 1 0 1 1 0
%e 1 0 1 1 0 1
%e 0 1 1 0 1 1
%e 1 1 0 1 1 0
%t f[i_, j_] := Mod[(i + j)^2, 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}]] (* A204435 *)
%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}] (* A204436 *)
%Y Cf. A204436.
%K nonn,tabl
%O 1
%A _Clark Kimberling_, Jan 15 2012
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