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%I #9 Mar 17 2014 01:08:10
%S 1,1,1,1,2,1,1,2,2,1,1,3,3,3,1,1,3,3,3,3,1,1,3,4,4,4,3,1,1,3,4,4,4,4,
%T 3,1,1,4,4,5,5,5,4,4,1,1,4,5,5,5,5,5,5,4,1,1,4,5,6,6,6,6,6,5,4,1,1,4,
%U 5,6,6,6,6,6,6,5,4,1,1,4,5,6,7,7,7,7,7,6,5,4,1,1,4,6,6,7,7,7,7,7,7,6,6,4,1,1
%N Triangle T(n,m) which contains in row n the rounded ordinate value at abscissa m along the upper rim of the circle with diameter n centered at (n/2, 1).
%C The points on a circle centered at (xmid,ymid) have ordinate values y = ymid + sqrt(r^2-(x-xmid)^2) for abscissae x, where r is the radius. Let xmid = r = n/2 and ymid = 1. Then T(n,m) is the rounded value of y as m=x runs through the integers from 0 (left rim of the circle) to d=n (right rim).
%e The fifth row is 1,3,3,3,3,1 because after rounding these values fit the diameter 5 circle most closely.
%e The table starts
%e 1;
%e 1,1;
%e 1,2,1;
%e 1,2,2,1;
%e 1,3,3,3,1;
%e 1,3,3,3,3,1;
%e 1,3,4,4,4,3,1;
%e 1,3,4,4,4,4,3,1;
%e 1,4,4,5,5,5,4,4,1;
%e 1,4,5,5,5,5,5,5,4,1;
%e 1,4,5,6,6,6,6,6,5,4,1;
%p A111007 := proc(n,m) 1+sqrt((n/2)^2-(m-n/2)^2) ; round(%) ; end proc: seq(seq(A111007(n,m),m=0..n),n=0..10) ; # _R. J. Mathar_, Jun 15 2010
%K nonn,tabl,easy
%O 0,5
%A _Ben Paul Thurston_, Nov 19 2006
%E Definition clarified, value at n=0 inserted by _R. J. Mathar_, Jun 15 2010
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