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A333519 Number of regions in a polygon whose boundary consists of n+2 equally space points around a semicircle and n+2 equally spaced points along the diameter (a total of 2n+2 points). See Comments for precise definition. 5
0, 2, 13, 48, 141, 312, 652, 1160, 1978, 3106, 4775, 6826, 9803, 13328, 17904, 23536, 30652, 38640, 48945, 60300, 74248, 89892, 108768, 128990, 153826, 180206, 211483, 245000, 284375, 325140, 374450, 425312, 484168, 545938, 616981, 690132, 775077, 862220 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A semi-circular polygon with 2n+2 points is created by placing n+2 equally spaced vertices along the semicircle's arc (including the two end vertices). Also place n+2 equally spaced vertices along the diameter (again including the same two end vertices). Now connect every pair of vertices by a straight line segment. The sequence gives the number of regions in the resulting figure.

LINKS

Lars Blomberg, Table of n, a(n) for n = 0..50

Scott R. Shannon, Illustration for n = 2.

Scott R. Shannon, Illustration for n = 3.

Scott R. Shannon, Illustration for n = 5.

Scott R. Shannon, Illustration for n = 10.

Scott R. Shannon, Illustration for n = 15.

Scott R. Shannon, Illustration for n = 20.

CROSSREFS

Cf. A007678, A290865, A255011, A332953, A333282, A334458, A334459.

Sequence in context: A117717 A176060 A168172 * A270294 A330539 A005584

Adjacent sequences:  A333516 A333517 A333518 * A333520 A333521 A333522

KEYWORD

nonn

AUTHOR

Scott R. Shannon and N. J. A. Sloane, Mar 26 2020

EXTENSIONS

a(21) and beyond from Lars Blomberg, May 01 2020

STATUS

approved

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Last modified September 26 01:25 EDT 2020. Contains 337346 sequences. (Running on oeis4.)