%I #12 Apr 08 2017 18:38:03

%S 0,5,20,160,1130,8927,71630,594405,5025740,43243674,377127756,

%T 3327001441,29634744950,266164547110,2407763862342,21918167505714,

%U 200631620380132,1845576127894008,17052050519557200,158176470846492722

%N Number of length n+1 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than 5.

%C Column 5 of A205341.

%H R. H. Hardin, <a href="/A205338/b205338.txt">Table of n, a(n) for n = 1..210</a>

%F a(n) = Sum_{i=1..n}((Sum_{l=0..i}(binomial(i,l)*(Sum_{j=0..(5*(i-l))/11}((-1)^j*binomial(i-l,j)*binomial(-l+5*(-l-2*j+i)-j+i-1,5*(-l-2*j+i)-j)))*(-1)^l))*a(n-i))/n, a(0)=1. - _Vladimir Kruchinin_, Apr 07 2017

%e Some solutions for n=5:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..5....5....5....2....5....5....4....2....3....2....2....2....4....1....3....1

%e ..8....6...10....3....8....4....6....1....5....5....6....5....7....4....1....4

%e ..3....9....9....0....5....0....2....5....0....4....1....3....4....5....2....7

%e ..1....4....5....3....2....2....3....2....1....3....4....4....2....3....1....3

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%o (Maxima)

%o a(n):=if n=0 then 1 else sum((sum(binomial(i,l)*(sum((-1)^j*binomial(i-l,j)*binomial(-l+5*(-l-2*j+i)-j+i-1,5*(-l-2*j+i)-j),j,0,(5*(i-l))/11))*(-1)^l,l,0,i))*a(n-i),i,1,n)/n; /* _Vladimir Kruchinin_, Apr 07 2017 */

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 26 2012