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Revision History for A372616

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Number of curved edges among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.
(history; published version)

#10 by Michael De Vlieger at Fri May 10 08:49:31 EDT 2024

STATUS

proposed

approved

#9 by Scott R. Shannon at Fri May 10 07:48:02 EDT 2024

STATUS

editing

proposed

#8 by Scott R. Shannon at Fri May 10 07:43:57 EDT 2024

CROSSREFS

Cf. A372614 (vertices), A372615 (regions), A372617 (k-gons), A372682 (number of circles), A371375, A356358, A360353.

Discussion

Fri May 10

07:48

Scott R. Shannon: Submitting A372614, A372615, A372616, A372617, A372682 together.

#7 by Scott R. Shannon at Fri May 10 07:21:53 EDT 2024

COMMENTS

See A372614 and A372615 for images of the circles.

#6 by Scott R. Shannon at Fri May 10 07:09:28 EDT 2024

CROSSREFS

Cf. A372614 (vertices), A372615 (regions), A372617 (k-gons), , A372682 (circles).

#5 by Scott R. Shannon at Fri May 10 07:07:51 EDT 2024

FORMULA

a(n) = A372614(n) + A372615(n) - 1 by Euler's formula.

#4 by Scott R. Shannon at Fri May 10 07:07:16 EDT 2024

NAME

Number of curved edges among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.

COMMENTS

A circle is constructed for every pair of the 3 + 3*n points, the first point defines the circle's center while the second the radius distance.

CROSSREFS

Cf. A372614 (vertices), A372615 (regions), A372617 (k-gons), , A372682 (circles).

#3 by Scott R. Shannon at Fri May 10 04:03:24 EDT 2024

DATA

12, 207, 1104, 4359, 14880, 32523, 73662, 121605, 223290, 329286, 554286, 722841, 1145091

#2 by Scott R. Shannon at Tue May 07 08:32:37 EDT 2024

NAME

allocated for Scott R. Shannon

edges

DATA

12, 207, 1104, 4359, 14880, 32523, 73662, 121605, 223290

OFFSET

0,1

CROSSREFS

Cf. A372614 (vertices), A372615 (regions), A372617 (k-gons).

KEYWORD

allocated

nonn,more

AUTHOR

Scott R. Shannon, May 07 2024

STATUS

approved

editing

#1 by Scott R. Shannon at Tue May 07 08:17:13 EDT 2024

NAME

allocated for Scott R. Shannon

KEYWORD

allocated

STATUS

approved