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).

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

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