cp's OEIS Frontend

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.

A260769 Certain directed lattice paths.

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%I A260769 #16 Jul 15 2022 05:31:43
%S A260769 1,3,15,84,491,2948,18018,111520,696739,4384668,27753110,176494640,
%T A260769 1126809230,7217773800,46364184420,298554038144,1926593569059,
%U A260769 12455864623020,80664529969422,523165672201744,3397648036150426,22092460470618328,143809661629562460
%N A260769 Certain directed lattice paths.
%C A260769 See Dziemianczuk (2014) for precise definition.
%H A260769 Lars Blomberg, <a href="/A260769/b260769.txt">Table of n, a(n) for n = 0..100</a>
%H A260769 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 A260769 See Dziemianczuk (2014) Equation (29a) with m=0.
%F A260769 From _Vaclav Kotesovec_, Jul 15 2022: (Start)
%F A260769 Recurrence: (n-1)*n*(100*n^2 - 410*n + 411)*a(n) = -10*(n-1)*(8*n - 25)*a(n-1) + 4*(1100*n^4 - 6710*n^3 + 14571*n^2 - 13303*n + 4267)*a(n-2) - 120*(n-2)*(2*n - 1)*a(n-3) + 16*(n-3)*(n-2)*(100*n^2 - 210*n + 101)*a(n-4).
%F A260769 a(n) ~ sqrt(1 + sqrt(phi)) * 2^(n-1) * phi^(5*(2*n + 1)/4) / (5^(1/4) * sqrt(Pi*n)), where phi = A001622 is the golden ratio. (End)
%K A260769 nonn
%O A260769 0,2
%A A260769 _N. J. A. Sloane_, Jul 30 2015
%E A260769 More terms from _Lars Blomberg_, Aug 01 2015