A325678 - OEIS

A325678

Maximum length of a composition of n such that every restriction to a subinterval has a different sum.

0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

A composition of n is a finite sequence of positive integers summing to n.

Also the maximum number of nonzero marks on a Golomb ruler of length n.

LINKS

Table of n, a(n) for n=0..83.

FORMULA

a(n) + 1 = A143824(n + 1).

MATHEMATICA

Table[Max[Length/@Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@ReplaceList[#, {___, s__, ___}:>Plus[s]]&]], {n, 0, 15}]