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 A374542 #13 Nov 21 2024 03:10:17 %S A374542 1,1,2,6,22,87,351,1416,5681,22660,89961,355924,1404839,5536143, %T A374542 21794634,85749490,337271186,1326421512,5216761708,20520185594, %U A374542 80733298320,317713643536,1250674963766,4924782835110,19398524629494,76434881013402,301270165265954 %N A374542 Number of length n inversion sequences avoiding the patterns 102 and 210. %H A374542 Benjamin Testart, <a href="/A374542/b374542.txt">Table of n, a(n) for n = 0..1600</a> %H A374542 Benjamin Testart, <a href="https://arxiv.org/abs/2407.07701">Completing the enumeration of inversion sequences avoiding one or two patterns of length 3</a>, arXiv:2407.07701 [math.CO], 2024. %F A374542 G.f: ((4*x - 1) * (4*x^4 - 22*x^3 + 25*x^2 - 9*x + 1) - (2*x - 1) * (x^2 - 5*x + 1) * (2*x^2 - 4*x + 1) * (1-4*x)^(1/2)) / (2*x^3 * (4*x - 1) * (x - 1)^2). %F A374542 D-finite with recurrence -(n+3)*(1514*n-13441)*a(n) +(16281*n^2-104929*n-159699)*a(n-1) +(-54702*n^2+377288*n-136533)*a(n-2) +(60299*n^2-430394*n+520290)*a(n-3) -6*(2*n-7)*(1697*n-7015)*a(n-4) +30*(-702*n+3361)=0. - _R. J. Mathar_, Jul 12 2024 %F A374542 a(n) ~ 2^(2*n+1)/(3*sqrt(Pi*n)). - _Vaclav Kotesovec_, Nov 21 2024 %Y A374542 Cf. A279555. %K A374542 nonn %O A374542 0,3 %A A374542 _Benjamin Testart_, Jul 12 2024