A357060 - OEIS

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A357060

Number of vertices in a square when n internal squares are drawn between the 4n points that divide each side into n+1 equal parts.

4, 8, 20, 40, 68, 88, 148, 168, 260, 296, 404, 436, 580, 632, 788, 840, 1028, 1072, 1300, 1384, 1604, 1688, 1940, 1972, 2308, 2408, 2708, 2808, 3140, 3220, 3604, 3696, 4084, 4232, 4628, 4716, 5188, 5336, 5764, 5908, 6404, 6496, 7060, 7224, 7732, 7928, 8468, 8524, 9220, 9368, 9988, 10216

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

OFFSET

0,1

COMMENTS

The even values of n that yield squares with non-simple intersections are 32, 38, 44, 50, 54, 62, 76, 90, 98, ... .

LINKS

Table of n, a(n) for n=0..51.

Scott R. Shannon, Image for n = 1.

Scott R. Shannon, Image for n = 2.

Scott R. Shannon, Image for n = 3.

Scott R. Shannon, Image for n = 5. This is the first term that forms squares with non-simple intersections.

Scott R. Shannon, Image for n = 10.

Scott R. Shannon, Image for n = 32. This is the first term with n mod 2 = 0 that forms squares with non-simple intersections.

Scott R. Shannon, Image for n = 200.

FORMULA

a(n) = A357061(n) - A357058(n) + 1 by Euler's formula.

Conjecture: a(n) = 4*n^2 + 4 for squares that only contain simple intersections when cut by n internal squares. This is never the case for odd n >= 5.

CROSSREFS

Cf. A357058 (regions), A357061 (edges), A355949, A355839, A355799, A357007 (triangle).

Sequence in context: A156303 A301138 A008136 * A254128 A047196 A009889

Adjacent sequences: A357057 A357058 A357059 * A357061 A357062 A357063

KEYWORD

nonn

AUTHOR

Scott R. Shannon, Sep 10 2022

STATUS

approved