OFFSET
0,4
COMMENTS
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 up to sign.
Also the number of minimal (most refined) compositions of n such that every restriction to a subinterval has a different sum.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..100
Eric Weisstein's World of Mathematics, Golomb Ruler.
EXAMPLE
The a(1) = 1 through a(8) = 8 maximal Golomb rulers:
{0,1} {0,2} {0,1,3} {0,1,4} {0,1,5} {0,1,4,6} {0,1,3,7} {0,1,3,8}
{0,2,3} {0,3,4} {0,2,5} {0,2,5,6} {0,1,5,7} {0,1,5,8}
{0,3,5} {0,2,3,7} {0,1,6,8}
{0,4,5} {0,2,6,7} {0,2,3,8}
{0,4,5,7} {0,2,7,8}
{0,4,6,7} {0,3,7,8}
{0,5,6,8}
{0,5,7,8}
The a(1) = 1 through a(10) = 16 minimal compositions:
(1) (2) (12) (13) (14) (132) (124) (125) (126) (127)
(21) (31) (23) (231) (142) (143) (135) (136)
(32) (214) (152) (153) (154)
(41) (241) (215) (162) (163)
(412) (251) (216) (172)
(421) (341) (234) (217)
(512) (243) (253)
(521) (261) (271)
(315) (316)
(324) (352)
(342) (361)
(351) (451)
(423) (613)
(432) (631)
(513) (712)
(531) (721)
(612)
(621)
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Accumulate/@Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@ReplaceList[#, {___, s__, ___}:>Plus[s]]&]]], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 13 2019
EXTENSIONS
a(21)-a(50) from Fausto A. C. Cariboni, Feb 22 2022
STATUS
approved