A103301 Number of perfect rulers with n segments (n>=0).

1, 1, 3, 9, 24, 88, 254, 1064, 1644, 3382, 4156, 8022, 26264, 52012, 25434, 8506, 5632, 6224, 12330, 34224, 108854, 103156, 75992, 86560, 69084

Offset: 0

Author

Peter Luschny, Feb 28 2005

Keywords

• nonn
• hard

Comments

For definitions, references and links related to complete rulers see A103294.

Examples

			a(3)=9 counts the perfect rulers with 3 segments, {[0,1,2,4],[0,2,3,4], [0,1,3,4],[0,1,3,5],[0,2,4,5],[0,1,2,5],[0,3,4,5],[0,1,4,6],[0,2,5,6]}.
		

Links

• F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, MRLA search results and source code, Nov 6 2020.
• F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, Large Minimum Redundancy Linear Arrays: Systematic Search of Perfect and Optimal Rulers Exploiting Parallel Processing, IEEE Open Journal of Antennas and Propagation, 2 (2021), 79-85.
• Index entries for sequences related to perfect rulers.

Crossrefs

Cf. A103300, A103297, A103296 (Complete rulers with n segments), A103299 (Optimal rulers with n segments).

Formula

a(n) = Sum_{i=A004137(n)+1..A004137(n+1)} A103300(i), n>=1.

Extensions

Terms a(19)-a(24) found by exhaustive search by Fabian Schwartau, Yannic Schröder, Lars Wolf, Joerg Schoebel, Feb 23 2021