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 A320034 #20 Apr 22 2019 18:10:36
%S A320034 1,1,1,2,3,3,5,6,7,7,6,9,11,8,8,9,11,9,11,9,12,9,8,9,14,6,9,5,11,6,11,
%T A320034 4,12,5,8,4,14,5,9,3,11,5,11,3,12,5,8,3,14,5,9,3,11,5,11,3,12,5,8,3,
%U A320034 14,5,9,3,11,5,11,3,12,5,8,3,14,5,9,3,11,5,11,3,12,5,8,3,14,5,9,3,11,5,11,3,12,5,8,3
%N A320034 a(n) is the number of integer partitions of n with largest part <= 6 for which the index of the seaweed algebra formed by the integer partition paired with its weight is 0.
%C A320034 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([_,_]), where [,] denotes the bracket multiplication on g.
%C A320034 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 A320034 a(n) is periodic with period 12 for n > 36.
%H A320034 Colin Barker, <a href="/A320034/b320034.txt">Table of n, a(n) for n = 1..1000</a>
%H A320034 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 A320034 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 A320034 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,0,0,0,1,0,1).
%F A320034 For n > 36: a(n)=14 if 1 == n (mod 12), a(n)=5 if 2,6,10 == n (mod 12), a(n)=9 if 3 == n (mod 12), a(n)=3 if 0,4,8 == n (mod 12), a(n)=11 if 5,7 == n (mod 12), a(n)=12 if 9 == n (mod 12), a(n)=8 if 11 == n (mod 12).
%F A320034 G.f.: x*(1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 7*x^6 + 8*x^7 + 10*x^8 + 10*x^9 + 9*x^10 + 11*x^11 + 9*x^12 + 8*x^13 + 7*x^14 + 4*x^15 + 6*x^16 + 2*x^17 + 5*x^18 + x^19 + 4*x^20 + x^21 + x^22 - 3*x^25 - 7*x^27 - 7*x^29 - 5*x^31 - 2*x^33 - 2*x^35 - x^37 - x^39 - x^41 - x^43) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)). - _Colin Barker_, Apr 21 2019
%t A320034 a[n_] := If[n <= 36, {1, 1, 1, 2, 3, 3, 5, 6, 7, 7, 6, 9, 11, 8, 8, 9, 11, 9, 11, 9, 12, 9, 8, 9, 14, 6, 9, 5, 11, 6, 11, 4, 12, 5, 8, 4}[[n]], Switch[ Mod[n, 12], 1, 14, 2|6|10, 5, 3, 9, 0|4|8, 3, 5|7, 11, 9, 12, 11, 8]]; Array[a, 100] (* _Jean-François Alcover_, Dec 08 2018 *)
%o A320034 (PARI) Vec(x*(1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 7*x^6 + 8*x^7 + 10*x^8 + 10*x^9 + 9*x^10 + 11*x^11 + 9*x^12 + 8*x^13 + 7*x^14 + 4*x^15 + 6*x^16 + 2*x^17 + 5*x^18 + x^19 + 4*x^20 + x^21 + x^22 - 3*x^25 - 7*x^27 - 7*x^29 - 5*x^31 - 2*x^33 - 2*x^35 - x^37 - x^39 - x^41 - x^43) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)) + O(x^100)) \\ _Colin Barker_, Apr 21 2019
%Y A320034 Cf. A319981, A319982, A320033, A320036.
%K A320034 nonn,easy
%O A320034 1,4
%A A320034 _Nick Mayers_, Oct 03 2018
%E A320034 Data corrected by _Jean-François Alcover_, Dec 08 2018