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 A307789 #20 Aug 29 2022 09:54:43
%S A307789 1,1,1,2,5,13,35,96,267,750,2123,6046,17303,49721,143365,414584,
%T A307789 1201917,3492117,10165779,29643870,86574831,253188111,741365049,
%U A307789 2173243128,6377181825,18730782252,55062586341,161995031226,476941691177,1405155255055
%N A307789 Number of valid hook configurations of permutations of [n] that avoid the patterns 231 and 1243.
%C A307789 Essentially the same as A005773. - _R. J. Mathar_, May 06 2019
%H A307789 Colin Defant, <a href="http://arxiv.org/abs/1904.10451">Motzkin intervals and valid hook configurations</a>, arXiv preprint arXiv:1904.10451 [math.CO], 2019.
%F A307789 G.f.: 1 + 2*x^2/(3*x - 1 + sqrt(1 - 2*x - 3*x^2)).
%F A307789 D-finite with recurrence: +(-n+1)*a(n) +2*(n-1)*a(n-1) +3*(n-3)*a(n-2)=0. - _R. J. Mathar_, Jan 27 2020
%F A307789 a(n) = Sum_{k=0..n-2} A064189(n-2,k) for n>=2. - _Alois P. Heinz_, Aug 29 2022
%Y A307789 Cf. A005773, A064189.
%K A307789 nonn
%O A307789 0,4
%A A307789 _Colin Defant_, Apr 28 2019