A396184 Irregular triangle read by rows: row 0 is 0, row n for n >= 1 is 6*n^2-3*n+k for k = 1..6*n.

0, 4, 5, 6, 7, 8, 9, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153

Offset

0,2

Comments

Walk along the hexagonal spiral (as in A395362), with its cells numbered starting at 0. Begin with no kings (the kings are Glinski kings, as in Glinski hexagonal chess). If the square you are at is not attacked by an existing king, place a king there, otherwise leave it empty. The sequence lists the indices divided by 2 of the squares occupied by the kings.

A Glinski king at cell 0 can move to any of 12 cells: 1,2,3,4,5,6, or 7,9,11,13,15,17. The first king is placed at cell a(0) = 0. The smallest unattacked cell is cell 8, so the next king is placed at cell a(1) = 8/2 = 4.

If we ignore the spiral structure the cells themselves form a copy of the A_2 hexagonal lattice, and the cells containing the kings form a sublattice of index 4.

Links

Table of n, a(n) for n=0..78.

N. J. A. Sloane, Sketch showing first 62 cells of the spiral. Black circles indicate the kings, X's indicate cells attacked by earlier kings.

Example

Triangle begins:
  0,
  4, 5, 6, 7, 8, 9,
  19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
  46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63,
  85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108,
  ...

Crossrefs

Cf. A094159, A195319, A158480, A395362.

Sequence in context: A214419 A189481 A123977 * A109602 A084991 A356824

Adjacent sequences: A396181 A396182 A396183 * A396185 A396186 A396187

Keyword

nonn,tabf

Author

Jonas Karlsson and N. J. A. Sloane, May 30 2026

Status

approved