A204258 -id:A204258 - cp's OEIS frontend

A204259 Matrix given by f(i,j) = 1 + [(2i+j) mod 3], by antidiagonals.

1, 2, 3, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 3, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3

Offset: 1

Clark Kimberling, Jan 14 2012

This data is used to specify the height of hexagonally packed cylinders in a triangle with open boundaries. Three cylinders that touch each other define a "triple" and water can be retained between these cylinders. A257594, A258445 and A259052 give a classification for such spaces. The links below ignore the inter-cylinder space retention and only consider the water retention above solid cylinders. - Craig Knecht, Jul 16 2015

			Northwest corner:
1 2 3 1 2 3 1 2
3 1 2 3 1 2 3 1
2 3 1 2 3 1 2 3
1 2 3 1 2 3 1 2
3 1 2 3 1 2 3 1
2 3 1 2 3 1 2 3

Craig Knecht, Water retention triple.
Craig Knecht, Row sums of numbers completely surrounded by larger numbers (water retention) in A204259 = A008611.
Wikipedia, Water retention on mathematical surfaces

Cf. A204260.

f[i_, j_] := 1 + Mod[2 i + j, 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, 12}, {i, 1, n}]]   (* A204259 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 20}]     (* A204258 *)

A204257 Matrix given by f(i,j)=1+[(i+2j) mod 3], by antidiagonals.

Original entry on oeis.org

1, 3, 2, 2, 1, 3, 1, 3, 2, 1, 3, 2, 1, 3, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 2, 1, 3, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2

Offset: 1

Clark Kimberling, Jan 14 2012

			Northwest corner:
1 3 2 1 3 2 1 3
2 1 3 2 1 3 2 1
3 2 1 3 2 1 3 2
1 3 2 1 3 2 1 3
2 1 3 2 1 3 2 1
3 2 1 3 2 1 3 2

Cf. A204258.

f[i_, j_] := 1 + Mod[i + 2 j, 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, 12}, {i, 1, n}]]  (* A204257 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 20}]  (* A204258 *)

cp's OEIS Frontend

A204259 Matrix given by f(i,j) = 1 + [(2i+j) mod 3], by antidiagonals.

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