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A363768 The values k such that a regular k-gon with all diagonals drawn contains more 3-sided cells than 4-sided cells. 1
3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 30, 32, 33, 34, 36, 38, 40, 41, 42, 43, 44, 45, 46, 48, 54, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 74, 76, 78, 80, 82, 84, 86, 88, 94, 96, 98, 102, 108, 114, 118, 120, 126, 128, 138, 144 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
It is extremely likely that the terms in the data section form the complete list of such k-gons, although this is unknown. If more terms do exist they are greater than 875.
The only known k-gon where the number of 3-sided and 4-sided cells is equal is the 39-gon.
LINKS
Scott R. Shannon, Image of the 6-gon. This is the first k-gon to contain both 3 and 4 sided cells and where there are more 3-sided cells than 4-sided cells.
Scott R. Shannon, Image of the 15-gon. This is the first k-gon that contains more 4-sided cells than 3-sided cells.
Scott R. Shannon, Image of the 39-gon. This is the only known k-gon that contains the same number of 3 and 4 sided cells. It is likely to be the only such k-gon.
EXAMPLE
6 is a term as a regular 6-gon with all diagonals drawn contains 18 3-sided cells and 6 4-sided cells.
144 is a term as a regular 144-gon with all diagonals drawn contains 6363936 3-sided cells and 6270048 4-sided cells. This is likely the last such k-gon.
CROSSREFS
Sequence in context: A118955 A191838 A333214 * A108473 A298113 A026447
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Jun 21 2023
STATUS
approved

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Last modified April 16 10:35 EDT 2024. Contains 371709 sequences. (Running on oeis4.)