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

3,1

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

Table of n, a(n) for n=3..30.

R. J. Mathar, Tile count in the interior of regular n-gons dissected by medians

Index to sequences on drawing diagonals in regular polygons

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

Crossrefs

Cf. A165217, A320431.

Sequence in context: A184852 A067926 A165217 * A075224 A364928 A042185

Adjacent sequences: A320419 A320420 A320421 * A320423 A320424 A320425

Keyword

nonn,more

Author

R. J. Mathar, Jan 08 2019

Status

approved