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%I #14 Dec 29 2022 06:37:26
%S 1,3,6,7,9,12,16,18,21,30,36,42,46,54,60,70,81,90,102,117,129,136,156,
%T 171,184,201,216,235,255,273,292,318,339,355,384,408,435,465,492,514,
%U 549,579,604,642,675,709,744,780,814,852,888,928,969,1008,1048,1095
%N Number of compositions of n into three parts, using only natural numbers not in A007283.
%C 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.
%C The sequence is 2-regular, and has a linear representation of size 311.
%H G. Dombi, <a href="https://eudml.org/doc/278550">Additive properties of certain sets</a>, Acta Arithmetica 103 (2002), 137-146.
%H Jeffrey Shallit, <a href="https://arxiv.org/abs/2212.12473">Counterexample to a Conjecture of Dombi in Additive Number Theory</a>, arXiv:2212.12473 [math.NT], 2022.
%e For n=3 the 7 compositions are (1,1,1) and the six permutations of (0,1,2).
%Y Cf. A007283.
%K nonn
%O 0,2
%A _Jeffrey Shallit_, Dec 23 2022