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 A133009 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). 5
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 LINKS David W. Wilson, Table of n, a(n) for n = 0..10000 Antoine Renard, Michel Rigo, and Markus A. Whiteland, q-Parikh Matrices and q-deformed binomial coefficients of words, arXiv:2402.05657 [cs.FL], 2024. See pp. 3, 12. C. Sándor, Partitions of natural numbers and their representation functions, INTEGERS 4 (2004), #A18. Jeffrey Shallit, Additive Number Theory via Automata and Logic, arXiv:2112.13627 [math.NT], 2021. CROSSREFS Cf. A000028, A000379, A000069, A001969, A133008. Sequence in context: A301391 A068696 A343388 * A210705 A291771 A186972 Adjacent sequences: A133006 A133007 A133008 * A133010 A133011 A133012 KEYWORD nonn AUTHOR David W. Wilson, Dec 21 2007 STATUS approved

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Last modified July 16 08:10 EDT 2024. Contains 374345 sequences. (Running on oeis4.)