A359263 Number of compositions of n into three parts, using only natural numbers not in A007283.

1, 3, 6, 7, 9, 12, 16, 18, 21, 30, 36, 42, 46, 54, 60, 70, 81, 90, 102, 117, 129, 136, 156, 171, 184, 201, 216, 235, 255, 273, 292, 318, 339, 355, 384, 408, 435, 465, 492, 514, 549, 579, 604, 642, 675, 709, 744, 780, 814, 852, 888, 928, 969, 1008, 1048, 1095

Offset

0,2

Comments

Strictly increasing, and hence the complement of A007283 gives a counterexample to a conjecture of Dombi (see Links) saying that a set with infinite complement cannot have its sequence of 3-compositions strictly increasing in cardinality.

The sequence is 2-regular, and has a linear representation of size 311.

Links

Table of n, a(n) for n=0..55.

G. Dombi, Additive properties of certain sets, Acta Arithmetica 103 (2002), 137-146.

Jeffrey Shallit, Counterexample to a Conjecture of Dombi in Additive Number Theory, arXiv:2212.12473 [math.NT], 2022.

Example

For n=3 the 7 compositions are (1,1,1) and the six permutations of (0,1,2).

Crossrefs

Cf. A007283.

Sequence in context: A085359 A231664 A087916 * A296693 A282585 A280210

Adjacent sequences: A359260 A359261 A359262 * A359264 A359265 A359266

Keyword

nonn

Author

Jeffrey Shallit, Dec 23 2022

Status

approved