cp's OEIS Frontend

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.

%I A193362 #16 Jul 22 2025 12:24:38
%S A193362 0,31,57,99,158,237,340,472,635,836,1075,1361,1696,2087,2538,3054,
%T A193362 3641,4306,5053,5891,6822,7857,9000,10260,11643,13156,14807,16605,
%U A193362 18556,20671,22954,25418,28069,30918,33973,37243,40738,44469,48444,52676
%N 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.
%D A193362 H. T. Croft, K. J. Falconer and R. K. Guy, "Unsolved Problems in Geometry", 1991, page 89.
%H A193362 A. P. Goucher, <a href="http://cp4space.wordpress.com/2012/12/20/dissecting-the-disc/">Dissecting the disc</a>, Complex Projective 4-Space.
%e A193362 For n = 2, the a(2) = 31 dissections of the disc into 6n = 12 curvilinear triangles are:
%e A193362 * 1 solution in which 1 piece does not touch the center;
%e A193362 * 5 solutions in which 2 pieces do not touch the center;
%e A193362 * 10 solutions in which 3 pieces do not touch the center;
%e A193362 * 10 solutions in which 4 pieces do not touch the center;
%e A193362 * 3 solutions in which 5 pieces do not touch the center;
%e A193362 * 2 symmetrical solutions, one of which is exceptional.
%e A193362 The 30 non-exceptional cases are given in the article 'Dissecting the disc'.
%t A193362 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}]
%K A193362 nonn,easy
%O A193362 1,2
%A A193362 _Adam P. Goucher_, Dec 20 2012