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 A084519 #27 Dec 11 2020 18:10:38
%S A084519 1,1,3,13,47,173,639,2357,8695,32077,118335,436549,1610471,5941181,
%T A084519 21917583,80856053,298285687,1100404333,4059496479,14975869477,
%U A084519 55247410055,203812962077,751885445295,2773777080149,10232728055191
%N A084519 Number of indecomposable ground-state 3-ball juggling sequences of period n.
%C A084519 This sequence counts the length n asynchronic site swaps given in A084511/A084512.
%C A084519 First differences of A084518. INVERTi transform of A084509. Cf. also A084529, A003319.
%C A084519 Equals left border of triangle A145463. - _Gary W. Adamson_, Oct 11 2008
%D A084519 Carsten Elsner, Dominic Klyve and Erik R. Tou, A zeta function for juggling sequences, Journal of Combinatorics and Number Theory, Volume 4, Issue 1, 2012, pp. 1-13; ISSN 1942-5600
%H A084519 Fan Chung, R. L. Graham, <a href="http://www.jstor.org/stable/27642443">Primitive juggling sequences</a>, Am. Math. Monthly 115 (3) (2008) 185-194
%H A084519 <a href="/index/J#Juggling">Index entries for sequences related to juggling</a>
%H A084519 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, 2, 2).
%F A084519 a(n) seems to satisfy the recurrence: a(1) = a(2) = 1, a(3) = 3 and a(n) = 3*a(n-1)+2*a(n-2)+2*a(n-3). If so, a(n) = floor(A*B^n+1/2) where B = 3.6890953... is the real positive root of x^3-3x^2-2x-2 = 0 and A = 0.0687059... is the real positive root of 118*x^3+118*x^2+35*x-3 = 0. - _Benoit Cloitre_, Jun 14 2003 [This conjecture is established in the Chung-Graham paper.]
%F A084519 G.f.: x*(1-2*x-2*x^2)/(1-3*x-2*x^2-2*x^3). - _Colin Barker_, Jan 14 2012
%p A084519 INVERTi([seq(A084509(n),n=1..80)]);
%p A084519 with(combinat); A084519 := proc(n) option remember; local c,i,k; A084509(n)-add(add(mul(A084519(i),i=c),c=composition(n,k)),k=2..n); end;
%t A084519 LinearRecurrence[{3,2,2},{1,1,3},30] (* _Harvey P. Dale_, Jul 20 2013 *)
%Y A084519 Cf. A145463. - _Gary W. Adamson_, Oct 11 2008
%K A084519 nonn
%O A084519 1,3
%A A084519 _Antti Karttunen_, Jun 02 2003