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 A260770 #15 Jul 15 2022 05:50:37 %S A260770 1,6,35,207,1251,7678,47658,298371,1880659,11918586,75871710, %T A260770 484793950,3107494430,19973075580,128678167220,830735862179, %U A260770 5372968238979,34807369089378,225818672567382,1466956891774602,9540909022501226,62119854068610436,404854330511525580 %N A260770 Certain directed lattice paths. %C A260770 See Dziemianczuk (2014) for precise definition. %H A260770 Lars Blomberg, <a href="/A260770/b260770.txt">Table of n, a(n) for n = 0..100</a> %H A260770 M. Dziemianczuk, <a href="http://arxiv.org/abs/1410.5747">On Directed Lattice Paths With Additional Vertical Steps</a>, arXiv preprint arXiv:1410.5747 [math.CO], 2014. %F A260770 See Dziemianczuk (2014) Equation (29a) with m=1. %F A260770 From _Vaclav Kotesovec_, Jul 15 2022: (Start) %F A260770 Recurrence: (n-2)*n*(n+1)*(100*n^3 - 510*n^2 + 677*n - 111)*a(n) = -6*n*(40*n^3 - 5*n^2 - 586*n + 863)*a(n-1) + 4*(n-1)*(1100*n^5 - 6710*n^4 + 12387*n^3 - 3775*n^2 - 8723*n + 5448)*a(n-2) - 72*(n-2)*(n-1)*(10*n^2 - 5*n - 24)*a(n-3) + 16*(n-3)*(n-2)*(n-1)*(100*n^3 - 210*n^2 - 43*n + 156)*a(n-4). %F A260770 a(n) ~ sqrt((4*phi^6 - 1)/5 + phi^(11/2)) * 2^(n-1) * phi^(5*n/2) / sqrt(Pi*n), where phi = A001622 is the golden ratio. (End) %K A260770 nonn %O A260770 0,2 %A A260770 _N. J. A. Sloane_, Jul 30 2015 %E A260770 More terms from _Lars Blomberg_, Aug 01 2015