login
A357008
Number of edges in an equilateral triangle when n internal equilateral triangles are drawn between the 3n points that divide each side into n+1 equal parts.
6
3, 9, 27, 57, 99, 135, 219, 297, 351, 489, 603, 645, 867, 1017, 1107, 1353, 1539, 1575, 1947, 2127, 2295, 2649, 2907, 3021, 3459, 3753, 3855, 4359, 4707, 4821, 5403, 5769, 5967, 6537, 6897, 6957, 7779, 8217, 8451, 9003, 9603, 9837, 10587, 11061, 11211, 12153, 12699, 12897, 13827, 14409, 14715
OFFSET
0,1
COMMENTS
See A356984 and A357007 for images of the triangles.
LINKS
FORMULA
a(n) = A356984(n) + A357007(n) - 1 by Euler's formula.
Conjecture: a(n) = 6*n^2 + 3 for equilateral triangles that only contain simple vertices when cut by n internal equilateral triangles. This is never the case if (n + 1) mod 3 = 0 for n > 3.
CROSSREFS
Cf. A356984 (regions), A357007 (vertices), A274586, A332376, A333027, A344896.
Sequence in context: A093665 A093546 A015955 * A097803 A227097 A201202
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Sep 08 2022
STATUS
approved