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

1,3

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.

Links

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

Example

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;

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.

Sequence in context: A163649 A110858 A008279 * A056043 A187005 A158497

Adjacent sequences: A239569 A239570 A239571 * A239573 A239574 A239575

Keyword

nonn,tabf

Author

Heinrich Ludwig, Mar 22 2014

Status

approved