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.

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

Author

Scott R. Shannon, Sep 08 2022

Keywords

• nonn

Comments

See A356984 and A357007 for images of the triangles.

Links

• Scott R. Shannon, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A356984 (regions), A357007 (vertices), A274586, A332376, A333027, A344896.

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.