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

1,2

Comments

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

Links

Table of n, a(n) for n=1..99.

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

Example

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

Mathematica

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 *)

Crossrefs

Cf. A204260.

Sequence in context: A367619 A097663 A247565 * A371888 A066517 A108132

Adjacent sequences: A204256 A204257 A204258 * A204260 A204261 A204262

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 14 2012

Status

approved