

A169942


Number of Golomb rulers of length n.


49



1, 1, 3, 3, 5, 7, 13, 15, 27, 25, 45, 59, 89, 103, 163, 187, 281, 313, 469, 533, 835, 873, 1319, 1551, 2093, 2347, 3477, 3881, 5363, 5871, 8267, 9443, 12887, 14069, 19229, 22113, 29359, 32229, 44127, 48659, 64789, 71167, 94625, 105699, 139119, 151145, 199657
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OFFSET

1,3


COMMENTS

Wanted: a recurrence. Are any of A169940A169954 related to any other entries in the OEIS?
Leading entry in row n of triangle in A169940. Also the number of Sidon sets A with min(A) = 0 and max(A) = n. Odd for all n since {0,n} is the only symmetric Golomb ruler, and reversal preserves the Golomb property. Bounded from above by A032020 since the ruler {0 < r_1 < ... < r_t < n} gives rise to a composition of n: (r_1  0, r_2  r_1, ... , n  r_t) with distinct parts.  Tomas Boothby, May 15 2012
Also the number of compositions of n such that every restriction to a subinterval has a different sum. This is a stronger condition than all distinct consecutive subsequences having a different sum (cf. A325676).  Gus Wiseman, May 16 2019


LINKS



FORMULA



EXAMPLE

For n=2, there is one Golomb Ruler: {0,2}. For n=3, there are three: {0,3}, {0,1,3}, {0,2,3}.  Tomas Boothby, May 15 2012
The a(1) = 1 through a(8) = 15 compositions such that every restriction to a subinterval has a different sum:
(1) (2) (3) (4) (5) (6) (7) (8)
(12) (13) (14) (15) (16) (17)
(21) (31) (23) (24) (25) (26)
(32) (42) (34) (35)
(41) (51) (43) (53)
(132) (52) (62)
(231) (61) (71)
(124) (125)
(142) (143)
(214) (152)
(241) (215)
(412) (251)
(421) (341)
(512)
(521)
(End)


MATHEMATICA

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@ReplaceList[#, {___, s__, ___}:>Plus[s]]&]], {n, 15}] (* Gus Wiseman, May 16 2019 *)


PROG

(Sage)
R = QQ['x']
return sum(1 for c in cartesian_product([[0, 1]]*n) if max(R([1] + list(c) + [1])^2) == 2)


CROSSREFS

Cf. A000079, A103295, A103300, A108917, A143824, A325466, A325545, A325676, A325678, A325679, A325683, A325686.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



