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 A320033 #15 Apr 21 2019 07:46:11
%S A320033 1,1,1,2,3,3,4,5,6,6,4,6,7,5,5,6,7,4,5,5,7,3,5,3,7,3,5,3,7,3,5,3,7,3,
%T A320033 5,3,7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3,
%U A320033 7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3,7,3,5,3
%N A320033 a(n) is the number of integer partitions of n with largest part <= 5 for which the index of the seaweed algebra formed by the integer partition paired with its weight is 0.
%C A320033 The index of a Lie algebra, g, is an invariant of the Lie algebra defined by min(dim(Ker(B_f)) where the min is taken over all linear functionals f on g and B_f denotes the bilinear form f([_,_]) were [,] denotes the bracket multiplication on g.
%C A320033 For seaweed subalgebras of sl(n), which are Lie subalgebras of sl(n) whose matrix representations are parametrized by an ordered pair of compositions of n, the index can be determined from a corresponding graph called a meander.
%C A320033 a(n) is periodic with period 4 for n > 20.
%H A320033 Colin Barker, <a href="/A320033/b320033.txt">Table of n, a(n) for n = 1..1000</a>
%H A320033 V. Coll, A. Mayers, N. Mayers, <a href="https://arxiv.org/abs/1809.09271">Statistics on integer partitions arising from seaweed algebras</a>, arXiv preprint arXiv:1809.09271 [math.CO], 2018.
%H A320033 V. Dergachev, A. Kirillov, <a href="https://www.emis.de/journals/JLT/vol.10_no.2/6.html">Index of Lie algebras of seaweed type</a>, J. Lie Theory 10 (2) (2000) 331-343.
%H A320033 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F A320033 For n > 20: a(n)=7 if 1 == n (mod 4), a(n)=3 if 2 == n (mod 4), a(n)=5 if 3 == n (mod 4), a(n)=3 if 0 == n (mod 4).
%F A320033 From _Colin Barker_, Apr 21 2019: (Start)
%F A320033 G.f.: x*(1 + x + x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 3*x^6 + 3*x^7 + 3*x^8 + 3*x^9 + x^11 + x^12 - x^13 + x^14 - x^17 - x^19 - x^21 - 2*x^23) / ((1 - x)*(1 + x)*(1 + x^2)).
%F A320033 a(n) = a(n-4) for n>24.
%F A320033 (End)
%t A320033 Join[{1, 1, 1, 2, 3, 3, 4, 5, 6, 6, 4, 6, 7, 5, 5, 6, 7, 4, 5, 5}, LinearRecurrence[{0, 0, 0, 1}, {7, 3, 5, 3}, 100]] (* _Jean-François Alcover_, Dec 07 2018 *)
%o A320033 (PARI) Vec(x*(1 + x + x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 3*x^6 + 3*x^7 + 3*x^8 + 3*x^9 + x^11 + x^12 - x^13 + x^14 - x^17 - x^19 - x^21 - 2*x^23) / ((1 - x)*(1 + x)*(1 + x^2)) + O(x^100)) \\ _Colin Barker_, Apr 21 2019
%Y A320033 Cf. A319981, A319982, A320034, A320036.
%K A320033 nonn
%O A320033 1,4
%A A320033 _Nick Mayers_, Oct 03 2018