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 A199711 Triangular array: T(n,k) gives the number of numerical semigroups of genus n and multiplicity k, (n>=1, k>=2). 1
 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 4, 4, 1, 1, 3, 6, 7, 5, 1, 1, 3, 7, 10, 11, 6, 1, 1, 3, 9, 13, 17, 16, 7, 1, 1, 4, 11, 16, 27, 28, 22, 8, 1, 1, 4, 13, 22, 37, 44, 44, 29, 9, 1, 1, 4, 15, 24, 49, 64, 72, 66, 37, 10, 1, 1, 5, 18, 32, 66, 85, 116, 116, 95, 46, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS A numerical semigroup is a subset S of N, the nonnegative integers, that is closed under addition, contains the element 0 and such that N-S is finite. The cardinality of N-S is called the genus of S. The least positive integer belonging to S is called the multiplicity of S. The number of numerical semigroups of genus n is A007323(n). LINKS V. Blanco, P. A. Garcia-Sanchez and J. Puerto, Computing the number of numerical semigroups using generating functions, arXiv:0901.1228v3 [math.CO], 2009. Nathan Kaplan, Counting Numerical Semigroups, arXiv:1707.02551 [math.CO], 2017. EXAMPLE Triangle begins .n\k.|..2....3....4....5....6....7....8....9...10 = = = = = = = = = = = = = = = = = = = = = = = = = ..1..|..1 ..2..|..1....1 ..3..|..1....2....1 ..4..|..1....2....3....1 ..5..|..1....2....4....4....1 ..6..|..1....3....6....7....5....1 ..7..|..1....3....7...10...11....6....1 ..8..|..1....3....9...13...17...16....7....1 ..9..|..1....4...11...16...27...28...22....8....1 ... T(3,3) = 2: The two numerical semigroups of genus 3 and multiplicity 3 are S = N - {1,2,4} and S = N - {1,2,5}. CROSSREFS Cf. A007323 (row sums). Sequence in context: A181322 A004070 A180562 * A048887 A047913 A152977 Adjacent sequences:  A199708 A199709 A199710 * A199712 A199713 A199714 KEYWORD nonn,tabl AUTHOR Peter Bala, Nov 09 2011 STATUS approved

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