A347750 Number of intersection points when every pair of vertices of a row of n adjacent congruent rectangles are joined by an infinite line.

0, 5, 17, 57, 133, 297, 525, 925, 1477, 2289, 3277, 4701, 6437, 8805, 11541, 14917, 18869, 23893, 29509, 36473, 44349, 53545, 63605, 75629, 88901, 104325, 120981, 139913, 160581, 184409, 209885, 238989, 270525, 305413, 342413, 383301, 426949, 475757, 527205, 583261, 642821, 708717, 777829

Offset

0,2

Links

Table of n, a(n) for n=0..42.

Scott R. Shannon, Image for n = 2.

Scott R. Shannon, Image for n = 3.

Scott R. Shannon, Image for n = 4.

Scott R. Shannon, Image for n = 5.

Scott R. Shannon, Image for n = 6.

Formula

a(n) = A347751(n) - A344993(n) + 1.

Example

a(1) = 5 as connecting the four vertices of a single rectangle forms one new vertex inside the rectangle, giving a total of 4 + 1 = 5 total intersection points.
a(2) = 17 as connecting the six vertices of two adjacent rectangles forms seven vertices inside the rectangles while also forming four vertices outside the rectangles. The total number of intersection points is then 6 + 7 + 4 = 17.
See the linked images for further examples.

Crossrefs

Cf. A344993 (number of polygons), A347751 (number of edges), A331755 (number of intersections on or inside the rectangles).

Sequence in context: A112410 A146271 A145371 * A112044 A027030 A033538

Adjacent sequences: A347747 A347748 A347749 * A347751 A347752 A347753

Keyword

nonn

Author

Scott R. Shannon and N. J. A. Sloane, Sep 12 2021

Status

approved