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%I #15 Mar 12 2017 16:40:20
%S 1,4,22,130,803,5085,32747,213419,1403399,9292850,61877337,413894378,
%T 2779029389,18719276722,126438191373,856054836170,5808041074705,
%U 39478084788582,268776967284806,1832579782914892,12511376749656415
%N Number of sequences of n integers p(i) i=0..n-1 with 0 <= p(i) <= 3*i and |p(i) - p(i-1)| <= 3.
%C Paths down an n-high rectangular-grid right triangle with interior neighbor fanout 2*3 + 1.
%C Column 3 of A180906.
%C Alternatively, this sequence corresponds to the number of nonnegative walks with n steps {-3,-2,-1,0,1,2,3} starting at the origin, ending at any altitude, and not going below the x-axis. - _David Nguyen_, Dec 01 2016
%H R. H. Hardin, <a href="/A180899/b180899.txt">Table of n, a(n) for n=1..100</a>
%H C. Banderier, C. Krattenthaler, A. Krinik, D. Kruchinin, V. Kruchinin, D. Nguyen, and M. Wallner, <a href="https://arxiv.org/abs/1609.06473">Explicit formulas for enumeration of lattice paths: basketball and the kernel method</a>, arXiv:1609.06473 [math.CO], 2016.
%K nonn
%O 1,2
%A _R. H. Hardin_, Sep 23 2010
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