A111007 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).

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, 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, 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

Offset

0,5

Comments

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).

Links

Table of n, a(n) for n=0..105.

Example

The fifth row is 1,3,3,3,3,1 because after rounding these values fit the diameter 5 circle most closely.
The table starts
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;
1,3,4,4,4,4,3,1;
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;

Maple

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

Crossrefs

Sequence in context: A134542 A106254 A117147 * A176353 A103691 A103441

Adjacent sequences: A111004 A111005 A111006 * A111008 A111009 A111010

Keyword

nonn,tabl,easy

Author

Ben Paul Thurston, Nov 19 2006

Extensions

Definition clarified, value at n=0 inserted by R. J. Mathar, Jun 15 2010

Status

approved