A383273 Triangle read by rows: T(n,k) is the number of ruler-and-compass constructions consisting of n-k lines and k circles with 0 <= k <= n.

1, 1, 2, 0, 2, 1, 0, 0, 12, 4, 0, 0, 45, 116, 44, 0, 0, 232, 1565, 3005, 1084, 0, 0, 1627, 34114, 166556, 249494, 91192, 0, 0, 21547

Offset: 0

Author

Peter Kagey, Apr 21 2025

Keywords

• nonn
• tabl
• hard
• more

Comments

Row sums are given by A383082.

Examples

			n\k | 0 1   2    3    4    5
----+--------------------------
  0 | 1
  1 | 1 2
  2 | 0 2    1
  3 | 0 0   12     4
  4 | 0 0   45   116     44
  5 | 0 0  232  1565   3005   1084
  6 | 0 0 1627 34114 166556 249494 91192
T(2,1) = 2 because there are two ruler-and-compass constructions with a line and a circle:
  A circle centered at (0,0) through (1,0) and a line through (0,0),(1,0).
  A circle centered at (1,0) through (0,0) and a line through (0,0),(1,0).
T(2,2) = 1 because there is one ruler-and-compass construction with two circles:
  A circle centered at (0,0) through (1,0) and a circle centered at (1,0) through (0,0).
		

Links

• Peter Kagey, Illustration of T(3,2) = 12 and T(3,3) = 4.

Crossrefs

Cf. A333944, A383082, A383083.

Formula

T(n,n) = A383083(n).