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A204553
Symmetric matrix: f(i,j)=floor[(2i+2j+2)/4]-floor[(i+j+1)/4], by (constant) antidiagonals.
3
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
OFFSET
1,7
COMMENTS
For n>=1, the number of occurrences of n is 16n-10. For a guide to related sequences and permanents, see A204551.
EXAMPLE
Northwest corner:
1 1 1 2 2 2 2 3 3
1 1 2 2 2 2 3 3 3
1 2 2 2 2 3 3 3 3
2 2 2 2 3 3 3 3 4
2 2 2 3 3 3 3 4 4
2 3 3 3 3 4 4 4 4
3 3 3 3 4 4 4 4 5
MATHEMATICA
f[i_, j_] :=
Floor[(2 i + 2 j + 2)/4] - Floor[(i + j + 1)/4];
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}]] (* A204553 *)
Permanent[m_] :=
With[{a = Array[x, Length[m]]},
Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 15}] (* A204554 *)
CROSSREFS
Sequence in context: A343743 A069926 A077429 * A214455 A060417 A097944
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 16 2012
STATUS
approved