A386560 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the number of finite regions created in the resulting graph.

4, 72, 424, 1396, 3536, 7292, 14272, 24332, 39356, 59920, 91348, 128084, 182664, 245804, 323116, 418552, 547820, 684680, 869388, 1060892, 1289564, 1560920

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Scott R. Shannon, Image for n = 1. In this and other images the integer coordinates are highlighted as white dots while the outer open regions, which are not counted, are darkened.

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

Formula

a(n) = A386561(n) - A386559(n) + 1 by Euler's formula.

Crossrefs

Cf. A386559 (vertices), A386561 (edges), A386562 (k-gons), A344993, A344857, A344279, A345459.

Sequence in context: A095385 A375251 A071683 * A192826 A190398 A003752

Adjacent sequences: A386557 A386558 A386559 * A386561 A386562 A386563

Keyword

nonn,more

Author

Scott R. Shannon, Jul 26 2025

Status

approved