A103300 Number of perfect rulers with length n.

1, 1, 1, 2, 3, 4, 2, 12, 8, 4, 38, 30, 14, 6, 130, 80, 32, 12, 500, 326, 150, 66, 18, 4, 944, 460, 166, 56, 12, 6, 2036, 890, 304, 120, 20, 10, 2, 2678, 974, 362, 100, 36, 4, 2, 4892, 2114, 684, 238, 68, 22, 4, 16318, 6350, 2286, 836, 330, 108, 24, 12, 31980, 12252

Offset

0,4

Comments

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

The values for n = 208-213 are 22,0,0,0,4,4 according to Arch D. Robison. The values for 199-207 are not yet known. - Peter Luschny, Feb 20 2014, Jun 28 2019

Zero values at 135, 136, 149, 150, 151, 164, 165, 166, 179, 180, 181, 195, 196, 209, 210, 211. - Ed Pegg Jr, Jun 23 2019 [These values were found by Arch D. Robison, see links. Peter Luschny, Jun 28 2019]

From Yannic Schröder, Feb 22 2021: (Start)

Zero values at 135, 136, 149, 150, 151, 164, 165, 166, 179, 180, 181, 195, 196 have been replaced with correct values using an additional mark.

A lower bound for 209 is 62, for 210 is 16, and for 211 is 204.

The verified value for 212 and for 213 is 4. (End)

Links

Peter Luschny (0..123), Arch D. Robison (124..198) and Fabian Schwartau and Yannic Schröder (199..208), Table of n, a(n) for n = 0..208

Peter Luschny, Perfect and Optimal Rulers.

Arch D. Robison, Parallel Computation of Sparse Rulers, Jan 14 2014.

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.

Formula

a(n) = T(n, A103298(n)) where the triangle T is described by A103294.

Example

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

Crossrefs

Cf. A004137 (Maximal number of edges in a graceful graph on n nodes).

Cf. A103301, A103297, A103298.

Sequence in context: A220335 A117009 A204842 * A305402 A213394 A363774

Adjacent sequences: A103297 A103298 A103299 * A103301 A103302 A103303

Keyword

hard,nonn,nice

Author

Peter Luschny, Feb 28 2005

Status

approved