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A309361 Numbers n such that the number of interior intersection points A091908(n) of the n-intersected triangle increases exactly by 1 when the subdivision of the triangle is refined from n-1 to n cutting line segments. 2
1, 3, 5, 7, 9, 11, 13, 17, 21, 25, 27, 31, 33, 37, 43, 49, 51, 53, 55, 57, 61, 67, 73, 81, 93, 97, 101, 107, 113, 115, 121, 123, 127, 133, 137, 141, 145, 147, 157, 163, 173, 177, 183, 185, 193, 201, 205, 211, 213, 217, 235, 241, 243, 249, 253, 257 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..56.

Hugo Pfoertner, Illustration of a(2)=3, A091908(3)=A091908(4)-1.

FORMULA

A091908(a(n) + 1) = A091908(a(n)) + 1.

EXAMPLE

a(1) = 1 corresponds to change from the triangle without cutting line segments and correspondingly A091908(1)=0 interior intersection points to the triangle where the sides are divided into 2 equal pieces and the 3 line segments connecting the midpoints of the sides with the opposite vertices cutting each other in one common point, the center of gravity. (A091908(2)=1). Thus A091908(2) - A091908(1) = 1 -> a(1) = 1.

a(2) = 3 because the trisected triangle has one less interior intersection point (A091908(3) = 12) than the 4-sected triangle (A091908(4) = 13) -> a(2) = 3.

CROSSREFS

Cf. A091908, A092098, A309360.

Sequence in context: A050150 A062090 A172095 * A133854 A239008 A291343

Adjacent sequences:  A309358 A309359 A309360 * A309362 A309363 A309364

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Jul 26 2019

STATUS

approved

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Last modified June 16 10:17 EDT 2021. Contains 345056 sequences. (Running on oeis4.)