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%I #18 Feb 18 2024 10:02:43
%S 0,0,0,1,0,1,1,0,1,2,1,1,2,1,1,4,1,2,3,1,3,3,2,4,3,2,3,5,2,5,5,0,5,6,
%T 3,5,5,3,4,8,4,4,6,5,5,7,6,4,7,6,5,9,5,7,8,4,7,10,7,5,10,5,5,16,5,6,
%U 11,5,9,11,8,8,10,8,8,13,7,11,12,4,12,12,8,13,10,9,11,12,10,12,12
%N One defining property of the sequences {A, B} = {A000069, A001969} is that they are the unique pair of sets complementary with respect to the nonnegative integers such that q(n) = |{x : x, y in A, x < y, x + y = n}| = |{x : x, y in B, x < y, x + y = n}| for all n >= 0. The present sequence gives the values of q(n).
%H David W. Wilson, <a href="/A133009/b133009.txt">Table of n, a(n) for n = 0..10000</a>
%H Antoine Renard, Michel Rigo, and Markus A. Whiteland, <a href="https://arxiv.org/abs/2402.05657">q-Parikh Matrices and q-deformed binomial coefficients of words</a>, arXiv:2402.05657 [cs.FL], 2024. See pp. 3, 12.
%H C. Sándor, <a href="http://math.colgate.edu/~integers/e18/e18.Abstract.html">Partitions of natural numbers and their representation functions</a>, INTEGERS 4 (2004), #A18.
%H Jeffrey Shallit, <a href="https://arxiv.org/abs/2112.13627">Additive Number Theory via Automata and Logic</a>, arXiv:2112.13627 [math.NT], 2021.
%Y Cf. A000028, A000379, A000069, A001969, A133008.
%K nonn
%O 0,10
%A _David W. Wilson_, Dec 21 2007
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