

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
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OFFSET

1,2


REFERENCES

H. T. Croft, K. J. Falconer and R. K. Guy, "Unsolved Problems in Geometry", 1991, page 89.


LINKS

Table of n, a(n) for n=1..40.
A. P. Goucher, Dissecting the disc, Complex Projective 4Space.


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 nonexceptional 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



