OFFSET
0,4
COMMENTS
For definitions, references and links related to complete rulers see A103294.
Also the number of compositions of n whose consecutive subsequence-sums cover an initial interval of the positive integers. For example, (2,3,1) is such a composition because (1), (2), (3), (3,1), (2,3), and (2,3,1) are subsequences with sums covering {1..6}. - Gus Wiseman, May 17 2019
a(n) ~ c*2^n, where 0.2427 < c < 0.2459. - Fei Peng, Oct 17 2019
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..49
Scott Harvey-Arnold, Steven J. Miller, and Fei Peng, Distribution of missing differences in diffsets, arXiv:2001.08931 [math.CO], 2020.
Peter Luschny, Perfect rulers
Hugo Pfoertner, Count complete rulers of given length. FORTRAN program.
Gus Wiseman, Illustration of A103295.
EXAMPLE
a(4) = 4 counts the complete rulers with length 4, {[0,2,3,4],[0,1,3,4],[0,1,2,4],[0,1,2,3,4]}.
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], SubsetQ[ReplaceList[#, {___, s__, ___}:>Plus[s]], Range[n]]&]], {n, 0, 15}] (* Gus Wiseman, May 17 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Feb 28 2005
EXTENSIONS
a(30)-a(36) from Hugo Pfoertner, Mar 17 2005
a(37)-a(38) from Hugo Pfoertner, Dec 10 2021
a(39) from Hugo Pfoertner, Dec 16 2021
STATUS
approved