

A006600


Total number of triangles visible in regular ngon with all diagonals drawn.
(Formerly M4513)


20



1, 8, 35, 110, 287, 632, 1302, 2400, 4257, 6956, 11297, 17234, 25935, 37424, 53516, 73404, 101745, 136200, 181279, 236258, 306383, 389264, 495650, 620048, 772785, 951384, 1167453, 1410350, 1716191, 2058848, 2463384, 2924000, 3462305, 4067028, 4776219, 5568786, 6479551
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OFFSET

3,2


COMMENTS

Place n equallyspaced points on a circle, join them in all possible ways; how many triangles can be seen?


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS



FORMULA



EXAMPLE

a(4) = 8 because in a quadrilateral the diagonals cross to make four triangles, which pair up to make four more.


MATHEMATICA

del[m_, n_]:=If[Mod[n, m]==0, 1, 0]; Tri[n_]:=n(n1)(n2)(n^3+18n^243n+60)/720  del[2, n](n2)(n7)n/8  del[4, n](3n/4)  del[6, n](18n106)n/3 + del[12, n]*33n + del[18, n]*36n + del[24, n]*24n  del[30, n]*96n  del[42, n]*72n  del[60, n]*264n  del[84, n]*96n  del[90, n]*48n  del[120, n]*96n  del[210, n]*48n; Table[Tri[n], {n, 3, 1000}] (* T. D. Noe, Dec 21 2006 *)


CROSSREFS



KEYWORD

nonn,easy,nice


AUTHOR



EXTENSIONS

a(3)a(8) computed by Victor Meally (personal communication to N. J. A. Sloane, circa 1975); later terms and recurrence from S. Sommars and T. Sommars.


STATUS

approved



