A384703 - OEIS

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A384703

On a 2 X n grid of vertices, draw a circle through every unordered triple of non-collinear vertices: a(n) is the number of distinct edges in the planar graph formed from the intersections of the circles.

6

0, 4, 54, 416, 2182, 7884, 23294, 56982, 126310, 253564, 477462, 844524, 1424316

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

OFFSET

1,2

COMMENTS

The edges being counted are of course arcs of circles.

LINKS

Table of n, a(n) for n=1..13.

Scott R. Shannon, Image for a(3) = 54.

FORMULA

a(n) = A384701(n) + A384702(n) - 1 by Euler's formula, for n > 1.

CROSSREFS

Cf. A384700 (circles), A384701 (vertices), A384702 (regions), A359571, A374827, A374339, A373108.

Sequence in context: A156469 A001545 A208954 * A269507 A302942 A292305

Adjacent sequences: A384700 A384701 A384702 * A384704 A384705 A384706

KEYWORD

nonn,more

AUTHOR

Scott R. Shannon and N. J. A. Sloane, Jun 07 2025

STATUS

approved