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

Offset: 0

Author

Gus Wiseman, May 13 2019

Keywords

• nonn

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.

Crossrefs

Run-lengths are A270813.

Cf. A000079, A007318, A103295, A108917, A143823, A169942.

Cf. A325466, A325676, A325677, A325679, A325681, A325683, A325687.

Programs

Mathematica

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

Formula

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