A334701 - OEIS

A334701

Consider the figure made up of a row of n adjacent congruent rectangles, with diagonals of all possible rectangles drawn; a(n) = number of interior vertices where exactly two lines cross.

1, 6, 24, 54, 124, 214, 382, 598, 950, 1334, 1912, 2622, 3624, 4690, 6096, 7686, 9764, 12010, 14866, 18026, 21904, 25918, 30818, 36246, 42654, 49246, 57006, 65334, 75098, 85414, 97384, 110138, 124726, 139642, 156286, 174018, 194106, 214570, 237534, 261666, 288686, 316770, 348048, 380798, 416524, 452794, 492830

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

It would be nice to have a formula or recurrence. - N. J. A. Sloane, Jun 22 2020

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..500

Lars Blomberg, Array (s,n) of the number of internal vertices where exactly s=2..501 lines cross in a figure made up of a row of n=1..500 adjacent congruent rectangles, with diagonals of all possible rectangles drawn. Rows are stored comma-separated.

Lars Blomberg, Scott R. Shannon, N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids, (2020). Also arXiv:2009.07918.

Scott R. Shannon, Colored illustration showing regions for n=1

Scott R. Shannon, Images of vertices for n=1.

Scott R. Shannon, Colored illustration showing regions for n=2