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

0,1

Comments

See A356984 and A357007 for images of the triangles.

Links

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

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

Adjacent sequences: A357005 A357006 A357007 * A357009 A357010 A357011

Keyword

nonn

Author

Scott R. Shannon, Sep 08 2022

Status

approved