A320422 The number of tiles inside a regular n-gon created by diagonals that run from each of the n vertices to the n-2 midpoints of opposite edges.

6, 25, 50, 145, 224, 497, 684, 1281, 1650, 2713, 3406, 5223, 6300, 9137, 10744, 14779, 17214, 23161, 26250, 34277, 38456, 49105, 54500, 68225, 75114, 92457, 101094, 122371

Offset: 3

Author

R. J. Mathar, Jan 08 2019

Keywords

• nonn
• more

Comments

Sequence proposed by Thomas Young: draw the regular n-gon and construct n*(n-2) diagonals that run from each of the n vertices to the n-2 points in the middle of the opposite edges, where opposite edges are those not adjacent to the vertex. Count the non-overlapping polygons inside the n-gon which have sides that are sections of the diagonals or sections of the n-gon edges.

Links

• R. J. Mathar, Tile count in the interior of regular n-gons dissected by medians
• Index to sequences on drawing diagonals in regular polygons

Crossrefs

Cf. A165217, A320431.

Formula

Conjecture: a(2n+1) = n*(2*n+1)*(4*n^2-3*n+5)/3. - Thomas Young (tyoung(AT)district16.org), Jan 05 2019