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 A108600 #9 Jan 12 2025 17:09:46 %S A108600 1,1,2,6,20,71,260,971,3674,14032,53968,208692,810492,3158760, %T A108600 12346628,48377494,189952216,747180999,2943648824,11612917815, %U A108600 45869337526,181372345723,717856746216,2843678131629,11273602645942,44725291921541,177551518494116,705264937798343 %N A108600 Number of freely braided permutations of length n; the freely braided permutations are those that avoid 3421, 4231, 4312 and 4321. %D A108600 R. M. Green and J. Losonczy, Freely braided elements of Coxeter groups, Ann. Comb. 6 (2002), 337-348. %D A108600 T. Mansour, On an open problem of Green and Losonczy: exact enumeration of freely braided permutations, Discrete Math. Comput. Sci. 6 (2004), 461-470. %H A108600 V. Vatter, <a href="http://www.math.rutgers.edu/~vatter/programs/wilfplus/freely-braided.html">Enumeration scheme for freely braided permutations</a>. %F A108600 G.f. (1-3*x-2*x^2+(1+x)*sqrt(1-4*x)) / (1-4*x-x^2+(1-x^2)*sqrt(1-4*x)). %F A108600 Conjecture: (1-n)*a(n) +(7*n-10)*a(n-1) +2*(1-4*n)*a(n-2) +8*(11-2*n)*a(n-3) +(n-1)*a(n-4) +3*(2-n)*a(n-5) +2*(11-2*n)*a(n-6)=0. - _R. J. Mathar_, Aug 24 2013 %e A108600 a(5)=71 because there are 71 permutations of length 5 that avoid 3421, 4231, 4312 and 4321. %K A108600 easy,nonn %O A108600 0,3 %A A108600 _Vincent Vatter_, Jun 11 2005 %E A108600 a(0)=1 prepended by _Alois P. Heinz_, Jan 12 2025