This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A086161 #27 May 02 2025 10:59:25 %S A086161 1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,11,11, %T A086161 11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19, %U A086161 19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,25 %N A086161 Number of monomial ideals in two variables x, y that are Artinian, integrally closed, of colength n and contain x^2. %C A086161 Alternatively, "concave partitions" of n with at most 2 parts, where a concave partition is defined by demanding that the monomial ideal, generated by the monomials whose exponents do not lie in the Ferrers diagram of the partition, is integrally closed. %D A086161 G. E. Andrews, The Theory of Partitions, Addison-Wesley Publishing Company, 1976. %D A086161 M. Paulsen and J. Snellman, Enumerativa egenskaper hos konkava partitioner (in Swedish), Department of Mathematics, Stockholm University. %H A086161 V. Crispin Quinonez, <a href="https://www2.math.su.se/reports/2002/7/2002-7.pdf">Integrally closed monomial ideals and powers of ideals</a>, Research Reports in Mathematics Number 7 2002, Department of Mathematics, Stockholm University. %H A086161 Jan Snellman and Michael Paulsen, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL7/Snellman/snellman2.html">Enumeration of Concave Integer Partitions</a>, J. Integer Seqs., Vol. 7, 2004. %H A086161 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1). %F A086161 G.f.: (1 + x^2 - x^3)/((1 - x)*(1 - x^3)). %F A086161 a(n) = A008620(n+1). - _R. J. Mathar_, Sep 12 2008 %F A086161 E.g.f.: (3*exp(x)*(3 + x) - 2*sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/2))/9. - _Stefano Spezia_, Feb 11 2023 %o A086161 (PARI) Vec((1+x^2-x^3)/((1-x)*(1-x^3)) + O(x^80)) \\ _Michel Marcus_, May 22 2015 %Y A086161 Cf. A008620, A084913, A086162, A086163. %K A086161 nonn,easy %O A086161 0,3 %A A086161 _Jan Snellman_, Aug 25 2003