cp's OEIS Frontend

For n<=3 the terms equal A274585(n). See A328526 for images of the triangular frame.

A equilateral triangular "frame" of size n is formed from a triangular grid consisting of an outer edge of (n+1) points with the central grid of (n-5)*(n-6)/2 points removed. If n is less than 4 then no points or triangles are removed, and a(n) = A092867(n). From now on we assume n >= 4.

If we focus on the triangles rather than the points, the frame consists of a grid of equilateral triangles with the central block of (n-3)^2 triangles removed.

The resulting structure has an outer perimeter with 3*n points and an inner perimeter with 3*n-9 points, for a total of 6*n-9 perimeter points. The frame itself is the strip equilateral triangles pointing in alternate directions between the inner and outer perimeters such that the frame thickness equals the height of one triangle.

Now join every pair of perimeter points, both inner and outer, by a line segment, provided the line remains inside the frame. The sequence gives the number of regions in the resulting figure.

Like the square frame of A331776 only regions with 3 or 4 edges are formed.

See A328526 for images of the triangular frame.