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 A086162 #33 May 02 2025 10:59:13
%S A086162 1,1,2,3,3,5,5,5,7,8,8,11,11,11,14,15,15,19,19,19,23,24,24,29,29,29,
%T A086162 34,35,35,41,41,41,47,48,48,55,55,55,62,63,63,71,71,71,79,80,80,89,89,
%U A086162 89,98,99,99,109,109,109,119,120,120,131,131,131,142,143,143,155
%N A086162 Number of monomial ideals in two variables x, y that are Artinian, integrally closed, of colength n and contain x^3.
%C A086162 Alternatively, "concave partitions" of n with at most 3 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 A086162 G. E. Andrews, The Theory of Partitions, Addison-Wesley Publishing Company, 1976.
%D A086162 M. Paulsen and J. Snellman, Enumerativa egenskaper hos konkava partitioner (in Swedish), Department of Mathematics, Stockholm University.
%H A086162 Robert Israel, <a href="/A086162/b086162.txt">Table of n, a(n) for n = 0..10000</a>
%H A086162 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 A086162 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 Seq., Vol. 7 (2004), Article 04.1.3.
%H A086162 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,0,1,-1,0,-1,1).
%F A086162 G.f.: (1+t^2+t^5-2*t^6-t^8+t^9)/((1-t)*(1-t^3)*(1-t^6)).
%p A086162 f:= gfun:-rectoproc({a(i+10)=a(i)-a(i+1)-a(i+3)+a(i+4)-a(i+6)+a(i+7)+a(i+9), seq(a(i)=[1, 1, 2, 3, 3, 5, 5, 5, 7, 8][i+1],i=0..9)},a(i),remember):
%p A086162 map(f, [$0..100]); # _Robert Israel_, May 22 2015
%t A086162 LinearRecurrence[{1, 0, 1, -1, 0, 1, -1, 0, -1, 1}, {1, 1, 2, 3, 3, 5, 5, 5, 7, 8}, 60] (* _Jean-François Alcover_, Aug 16 2022 *)
%o A086162 (PARI) Vec((1+t^2+t^5-2*t^6-t^8+t^9)/((1-t)*(1-t^3)*(1-t^6)) + O(t^80)) \\ _Michel Marcus_, May 22 2015
%Y A086162 Cf. A084913, A086161, A086163.
%K A086162 nonn,easy
%O A086162 0,3
%A A086162 _Jan Snellman_, Aug 25 2003