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

Author

Jeffrey Shallit, Dec 23 2022

Keywords

• nonn

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.

Examples

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

Links

• 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.

Crossrefs

Cf. A007283.