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A367015
Number of regions formed after n points have been placed in general position on each edge of the triangle in A365929.
8
1, 4, 28, 136, 445, 1126, 2404, 4558, 7921, 12880, 19876, 29404, 42013, 58306, 78940, 104626, 136129, 174268, 219916, 274000, 337501, 411454, 496948, 595126, 707185, 834376, 978004, 1139428, 1320061, 1521370, 1744876, 1992154, 2264833, 2564596, 2893180, 3252376, 3644029, 4070038
OFFSET
0,2
COMMENTS
See A365929 for more information.
LINKS
Scott R. Shannon, Image for n = 2.
Scott R. Shannon, Image for n = 3. Note that although the number of k-gons will vary as the edge points change position the total number of regions will stay constant (at 136 for n = 3) as long as all internal vertices remain simple.
FORMULA
Conjecture: a(n) = (9*n^4 - 12*n^3 + 15*n^2 + 4)/4.
a(n) = A366932(n) - 3*A366478(n) + 1 by Euler's formula.
CROSSREFS
Cf. A365929 (internal vertices), A366932 (edges), A366478 (vertices/3).
Sequence in context: A270275 A296638 A270721 * A377885 A270892 A271603
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Nov 01 2023
STATUS
approved