A036501 Number of inequivalent Golomb rulers with n marks and shortest length.

1, 1, 1, 2, 4, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1

Offset

2,4

Comments

From Gus Wiseman, May 31 2019: (Start)

A Golomb ruler of length n is a subset of {0..n} containing 0 and n and such that every pair of distinct terms has a different difference. For example, the a(2) = 1 through a(8) = 1 Golomb rulers are:

2: {0,1}

3: {0,1,3}

4: {0,1,4,6}

5: {0,1,4,9,11}

5: {0,2,7,8,11}

6: {0,1,4,10,12,17}

6: {0,1,4,10,15,17}

6: {0,1,8,11,13,17}

6: {0,1,8,12,14,17}

7: {0,1,4,10,18,23,25}

7: {0,1,7,11,20,23,25}

7: {0,2,3,10,16,21,25}

7: {0,2,7,13,21,22,25}

7: {0,1,11,16,19,23,25}

8: {0,1,4,9,15,22,32,34}

Also half the number of length-(n - 1) compositions of A003022(n) such that every consecutive subsequence has a different sum. For example, the a(2) = 1 through a(8) = 1 compositions are (A = 10):

2: (1)

3: (1,2)

4: (1,3,2)

5: (1,3,5,2)

5: (2,5,1,3)

6: (1,3,6,2,5)

6: (1,3,6,5,2)

6: (1,7,3,2,4)

6: (1,7,4,2,3)

7: (1,3,6,8,5,2)

7: (1,6,4,9,3,2)

7: (2,1,7,6,5,4)

7: (2,5,6,8,1,3)

7: (1,A,5,3,4,2)

8: (1,3,5,6,7,A,2)

(End)

Links

Table of n, a(n) for n=2..19.

Anonymous, In Search Of The Optimal 20, 21 and 22 Mark Golomb Rulers

Distributed.Net, Project OGR

J. B. Shearer, Table of known optimal Golomb rulers

Eric Weisstein's World of Mathematics, Golomb Ruler

Index entries for sequences related to Golomb rulers

Crossrefs

Cf. A003022, A039953, A054578, A108917, A143823, A169942, A270813, A325677, A325683.

Sequence in context: A173163 A021412 A258066 * A225153 A360108 A308319

Adjacent sequences: A036498 A036499 A036500 * A036502 A036503 A036504

Keyword

nonn,hard,nice,more

Author

N. J. A. Sloane

Status

approved