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

0,4

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}]

Crossrefs

Run-lengths are A270813.

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

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

Sequence in context: A088519 A135034 A003059 * A247189 A192002 A263270

Adjacent sequences: A325675 A325676 A325677 * A325679 A325680 A325681

Keyword

nonn

Author

Gus Wiseman, May 13 2019

Status

approved