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 A193362 Numbers of ways in which a unit disc can be dissected into 6n curvilinear triangles, at least one of which does not contain the center 0
 0, 31, 57, 99, 158, 237, 340, 472, 635, 836, 1075, 1361, 1696, 2087, 2538, 3054, 3641, 4306, 5053, 5891, 6822, 7857, 9000, 10260, 11643, 13156, 14807, 16605, 18556, 20671, 22954, 25418, 28069, 30918, 33973, 37243, 40738, 44469, 48444, 52676 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES H. T. Croft, K. J. Falconer and R. K. Guy, "Unsolved Problems in Geometry", 1991, page 89. LINKS A. P. Goucher, Dissecting the disc, Complex Projective 4-Space. EXAMPLE For n = 2, the a(2) = 31 dissections of the disc into 6n = 12 curvilinear triangles are: * 1 solution in which 1 piece does not touch the center; * 5 solutions in which 2 pieces do not touch the center; * 10 solutions in which 3 pieces do not touch the center; * 10 solutions in which 4 pieces do not touch the center; * 3 solutions in which 5 pieces do not touch the center; * 2 symmetrical solutions, one of which is exceptional. The 30 non-exceptional cases are given in the article 'Dissecting the disc'. MATHEMATICA Table[If[n==1, 0, Boole[n==2]+1+2 n+1+(3 n^2+3 n+2)/2+Floor[(2 n^3+6 n^2+7 n+6)/6]+Floor[(n^4+10 n^3+35 n^2+50 n+120)/120]+1], {n, 1, 100}] CROSSREFS Sequence in context: A045116 A092227 A220539 * A293345 A096453 A218794 Adjacent sequences:  A193359 A193360 A193361 * A193363 A193364 A193365 KEYWORD nonn,easy AUTHOR Adam P. Goucher, Dec 20 2012 STATUS approved

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Last modified September 30 14:57 EDT 2020. Contains 337439 sequences. (Running on oeis4.)