A249752 Triangle read by rows: T(n,k) = number of arrangements of n circles in the affine plane having k outer circles.

1, 1, 2, 3, 5, 6, 14, 52, 60, 47

Offset: 1

Author

Omar E. Pol, Dec 14 2014

Keywords

• nonn
• tabl
• hard
• more

Comments

Consider the arrangements of n circles described in A250001.

T(n,k) is the number of arrangements of n circles in the affine plane whose perimeters are formed with parts from k circles. - Omar E. Pol, Aug 09 2015

From Omar E. Pol, Jul 06 2016: (Start)

Observation 1: column 1 gives A250001, at least if 1<=n<=4.

Observation 2: sum of n-th row = T(n+1,1), at least if 1<=n<=3. (End)

Examples

			Triangle begins:
1;
1,   2;
3,   5,  6;
14, 52, 60, 47;
...
		

Crossrefs

Sum of n-th row = A250001(n).

Leading diagonal gives A274702.

Cf. A252158, A261070, A274776, A274777.

Extensions

Corrected a(5)-a(6) and added a(7)-a(10) from Omar E. Pol, Oct 13 2015