A358330 -id:A358330 - cp's OEIS frontend

A358333 By concatenating the standard compositions for each part of the n-th standard composition, we get a sequence of length a(n). Row-lengths of A357135.

0, 1, 1, 2, 2, 2, 2, 3, 1, 3, 2, 3, 3, 3, 3, 4, 2, 2, 3, 4, 3, 3, 3, 4, 2, 4, 3, 4, 4, 4, 4, 5, 2, 3, 2, 3, 4, 4, 4, 5, 2, 4, 3, 4, 4, 4, 4, 5, 3, 3, 4, 5, 4, 4, 4, 5, 3, 5, 4, 5, 5, 5, 5, 6, 3, 3, 3, 4, 3, 3, 3, 4, 3, 5, 4, 5, 5, 5, 5, 6, 3, 3, 4, 5, 4, 4, 4

Offset: 0

Gus Wiseman, Nov 10 2022

nonn

The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.

			Composition 92 in standard order is (2,1,1,3), with compositions ((2),(1),(1),(1,1)) so a(92) = 5.

Gus Wiseman, Statistics, classes, and transformations of standard compositions

See link for sequences related to standard compositions (A066099).
Dominates A000120.
Row-lengths of A357135, which is ranked by A357134.
A related sequence is A358330.
Cf. A001511, A029931, A048896, A058891, A070939, A096111, A333766, A357137, A357139, A357186, A357187.

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
Length/@Table[Join@@stc/@stc[n],{n,0,100}]

Sum of A000120 over row n of A066099.

cp's OEIS Frontend

A358333 By concatenating the standard compositions for each part of the n-th standard composition, we get a sequence of length a(n). Row-lengths of A357135.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula