A353392 Number of compositions of n whose own run-lengths are a consecutive subsequence.

1, 1, 0, 0, 1, 2, 2, 2, 2, 8, 12, 16, 20, 35, 46, 59, 81, 109, 144, 202, 282

Offset

0,6

Links

Table of n, a(n) for n=0..20.

Example

The a(0) = 0 through a(10) = 12 compositions (empty columns indicated by dots, 0 is the empty composition):
  0  1  .  .  22  122  1122  11221  21122  333     1333
                  221  2211  12211  22112  22113   2233
                                           22122   3322
                                           31122   3331
                                           121122  22114
                                           122112  41122
                                           211221  122113
                                           221121  131122
                                                   221131
                                                   311221
                                                   1211221
                                                   1221121

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], #=={}||MemberQ[Join@@Table[Take[#, {i, j}], {i, Length[#]}, {j, i, Length[#]}], Length/@Split[#]]&]], {n, 0, 15}]

Crossrefs

The non-consecutive version for partitions is A325702.

The non-consecutive version is A353390, ranked by A353402.

The non-consecutive recursive version is A353391, ranked by A353431.

The non-consecutive reverse version is A353403.

The recursive version is A353430.

These compositions are ranked by A353432.

A003242 counts anti-run compositions, ranked by A333489.

A011782 counts compositions.

A169942 counts Golomb rulers, ranked by A333222.

A325676 counts knapsack compositions, ranked by A333223.

A329738 counts uniform compositions, partitions A047966.

A329739 counts compositions with all distinct run-lengths.

Cf. A008965, A032020, A103295, A103300, A114901, A238279, A324572, A325705, A333224, A333755, A351013, A353401.

Sequence in context: A152660 A339163 A058787 * A360310 A085056 A371619

Adjacent sequences: A353389 A353390 A353391 * A353393 A353394 A353395

Keyword

nonn,more

Author

Gus Wiseman, May 15 2022

Status

approved