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%I #17 Feb 08 2016 11:01:18
%S 0,0,0,0,0,4,27,120,440,1440,4368,12544,34560,92160,239360,608256,
%T 1517568,3727360,9031680,21626880,51249152,120324096,280166400,
%U 647495680,1486356480,3391094784,7693402112,17364418560,39007027200,87241523200,194330492928
%N Expansion of x^5*(4 - 5*x)/(1 - 2*x)^4.
%C a(n) is the number of North-East lattice paths from (0,0) to (n,n) that have exactly two east steps below y = x - 1 and exactly one east step above y = x+1. Details can be found in Section 4.1 in Pan and Remmel's link.
%H Colin Barker, <a href="/A268598/b268598.txt">Table of n, a(n) for n = 0..1000</a>
%H Ran Pan, Jeffrey B. Remmel, <a href="http://arxiv.org/abs/1601.07988">Paired patterns in lattice paths</a>, arXiv:1601.07988 [math.CO], 2016.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).
%F G.f.: x^5*(4 - 5*x)/(1 - 2*x)^4.
%F From _Colin Barker_, Feb 08 2016: (Start)
%F a(n) = 2^(n-7)*(n-4)*(n-3)*(n+3) for n>2.
%F a(n) = 8*a(n-1)-24*a(n-2)+32*a(n-3)-16*a(n-4) for n>3. (End)
%o (PARI) concat(vector(5), Vec((4-5*x)*x^5/(1-2*x)^4 + O(x^40))) \\ _Michel Marcus_, Feb 08 2016
%Y Cf. A268462, A268586, A268587.
%K nonn,easy
%O 0,6
%A _Ran Pan_, Feb 08 2016
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