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A357197
Number of vertices in a hexagon when n internal hexagons are drawn between the 6n points that divide each side into n+1 equal parts.
4
6, 12, 30, 60, 102, 156, 222, 300, 390, 468, 606, 708, 870, 1020, 1152, 1356, 1542, 1740, 1950, 2112, 2406, 2652, 2910, 3072, 3462, 3756, 4062, 4350, 4710, 4974, 5406, 5772, 6126, 6540, 6918, 7260, 7782, 8220, 8646, 8946, 9606, 10032, 10590, 11052, 11568, 12156, 12702, 13116, 13830, 14388
OFFSET
0,1
COMMENTS
Unlike similar dissections of the triangle and square, see A357007 and A357060, there is no obvious pattern for n values that yield hexagons with non-simple intersections; these n values begin 9, 11, 14, 19, 23, 27, 29, 32, 34, 35, 38, 39, 41, 43, ... .
LINKS
Scott R. Shannon, Image for n = 1.
Scott R. Shannon, Image for n = 2.
Scott R. Shannon, Image for n = 5.
Scott R. Shannon, Image for n = 9. This is the first term that forms hexagons with non-simple intersections.
Scott R. Shannon, Image for n = 50.
Scott R. Shannon, Image for n = 150.
FORMULA
a(n) = A357198(n) - A357196(n) + 1 by Euler's formula.
Conjecture: a(n) = 6*n^2 + 6 for hexagons that only contain simple intersections when cut by n internal hexagons.
CROSSREFS
Cf. A357196 (regions), A357198 (edges), A330846, A357007 (triangle), A357060 (square).
Sequence in context: A036690 A229746 A256579 * A322374 A351694 A014131
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Sep 17 2022
STATUS
approved