A180739 Number of numerical semigroups of multiplicity n and genus n+2.

1, 2, 6, 10, 17, 28, 44, 66, 95, 132, 178, 234, 301, 380, 472, 578, 699, 836, 990, 1162, 1353, 1564, 1796, 2050, 2327, 2628, 2954, 3306, 3685, 4092, 4528, 4994, 5491, 6020, 6582, 7178, 7809, 8476, 9180, 9922, 10703, 11524, 12386, 13290, 14237, 15228, 16264

Offset

2,2

Links

Table of n, a(n) for n=2..48.

Victor Blanco, Pedro A. Garcia-Sanchez, and Justo Puerto, Computing the number of numerical semigroups using generating functions, arXiv:0901.1228 [math.CO], 2009.

Nathan Kaplan, Counting Numerical Semigroups, Amer. Math. Monthly, 124 (2017), 862-875; arXiv:1707.02551 [math.CO], 2017.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = A060163(n-2) for n > 3. [follows from Kaplan's Theorem 2] - Andrei Zabolotskii, Oct 31 2025

Crossrefs

A diagonal of A199711.

Cf. A007323, A060163, A000124 (another diagonal).

Sequence in context: A099540 A190695 A238377 * A396420 A274679 A229218

Adjacent sequences: A180736 A180737 A180738 * A180740 A180741 A180742

Keyword

nonn,easy

Author

Jonathan Vos Post, Jan 22 2011

Extensions

Terms a(14) onwards added, name and offset edited by Andrei Zabolotskii, Oct 31 2025

Status

approved