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Number of sequences of n integers p(i) i=0..n-1 with 0 <= p(i) <= 4*i and |p(i) - p(i-1)| <= 4.
1

%I #20 Mar 12 2017 16:42:01

%S 1,5,35,265,2100,17075,141246,1182719,9994086,85049639,727865758,

%T 6257933219,54010196582,467657712902,4060558796894,35341693437365,

%U 308249001184768,2693524485431382,23575195919671458,206647076624751357

%N Number of sequences of n integers p(i) i=0..n-1 with 0 <= p(i) <= 4*i and |p(i) - p(i-1)| <= 4.

%C Paths down an n-high rectangular-grid right triangle with interior neighbor fanout 2*4 + 1.

%C Column 4 of A180906.

%C Alternatively, this sequence corresponds to the number of nonnegative walks with n steps {-4,-3,-2,-1,0,1,2,3,4} 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="/A180900/b180900.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