A239572 Triangle T(n, k) = Numbers of non-equivalent (mod D_3) ways to place k points on a triangular grid of side n so that no two of them are adjacent. Triangle read by rows.

1, 1, 2, 2, 1, 3, 6, 6, 1, 4, 16, 32, 24, 7, 1, 5, 32, 113, 200, 176, 66, 6, 7, 60, 329, 1053, 1976, 2096, 1162, 302, 34, 2, 8, 100, 790, 3932, 12565, 25676, 32963, 25638, 11294, 2493, 222, 7, 10, 160, 1702, 11988, 57275, 187984, 425329, 658608, 684671, 462519

Offset: 1

Author

Heinrich Ludwig, Mar 22 2014

Keywords

• nonn
• tabf

Comments

Triangle T(n, k) is irregularly shaped: 1 <= k <= A239438(n). First row corresponds to n = 1.

The maximal number of points that can be placed on a triangular grid of side n so that no two of them are adjacent is given by A239438(n).

Without the restriction "non-equivalent (mod D_3)" numbers are given by A239567.

Examples

			Triangle begins
  1;
  1;
  2,   2,   1;
  3,   6,   6,    1;
  4,  16,  32,   24,     7,     1;
  5,  32, 113,  200,   176,    66,     6;
  7,  60, 329, 1053,  1976,  2096,  1162,   302,    34,    2;
  8, 100, 790, 3932, 12565, 25676, 32963, 25638, 11294, 2493, 222, 7;
		

Links

• Heinrich Ludwig, Table of n, a(n) for n = 1..136

Crossrefs

Cf. A239438, A239567.

Column 1 is A001399,

Column 2 is A032091,

Column 3 is A239573,

Column 4 is A239574,

Column 5 is A239575,

Column 6 is A279446.