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, 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

Offset: 1

Author

Adam P. Goucher, Dec 20 2012

Keywords

• nonn
• easy

Examples

			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'.
		

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.

Programs

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}]