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A274585
Total number of vertices formed by intersections among sides and straight "chords" in a right triangle when each side is divided by vertices into n equal segments.
13
1, 3, 10, 58, 178, 558, 1255, 2532, 4786, 7804, 12292, 18966, 28540, 39117, 56107, 73924, 96010, 124704, 164815, 203316, 258706, 311296, 377998, 458862, 560827, 649011, 775336, 908974, 1056604, 1215174, 1428283, 1607964, 1866103, 2111587, 2399647, 2694115, 3040309, 3356544, 3811501, 4253191, 4720222, 5180589, 5806813, 6325035, 7036081, 7691035, 8392174, 9180471, 10136431, 10894698, 11930983
OFFSET
0,2
COMMENTS
Total number of points at intersections of sides/"chords" for the triangle in A092866(n).
LINKS
Scott R. Shannon, Image for n = 2.
Scott R. Shannon, Image for n = 3.
Scott R. Shannon, Image for n = 4.
Scott R. Shannon, Image for n = 5.
Scott R. Shannon, Image for n = 6.
Scott R. Shannon, Image for n = 10.
FORMULA
a(n) = A092866(n) + 3n.
By the Euler characteristic, a(n) = A274586(n) - A092867(n) + 1.
CROSSREFS
KEYWORD
nonn
AUTHOR
Cynthia Miaina Rasamimanananivo and Max Alekseyev, Jun 29 2016, Sep 02 2016
EXTENSIONS
a(0) = 1 added by N. J. A. Sloane, Jan 22 2022
STATUS
approved