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A204435
Symmetric matrix: f(i,j)=((i+j)^2 mod 3), read by (constant) antidiagonals.
15
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, 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, 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
OFFSET
1
COMMENTS
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:
Matrix..............Permanent of n-th submatrix
A204435=D204439.....A204436
A204437=D204435.....A204438
A204439=D204437.....A204439
A204441=D204447.....A204442
A204443=D204441.....A204444
A204445=D204443.....A204446
A204447=D204445.....A204448
Homer and Goldman mention this as an example of a two-dimensional recurrence. - N. J. A. Sloane, Aug 29 2018
REFERENCES
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.
EXAMPLE
Northwest corner:
1 0 1 1 0 1
0 1 1 0 1 1
1 1 0 1 1 0
1 0 1 1 0 1
0 1 1 0 1 1
1 1 0 1 1 0
MATHEMATICA
f[i_, j_] := Mod[(i + j)^2, 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}]] (* A204435 *)
Permanent[m_] :=
With[{a = Array[x, Length[m]]},
Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 22}] (* A204436 *)
CROSSREFS
Cf. A204436.
Sequence in context: A373136 A285427 A285621 * A331313 A267155 A204445
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 15 2012
STATUS
approved