Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
proposed
approved
editing
proposed
Number of length n+1 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than 5.
Column 5 of A205341.
Some solutions for n=5:
proposed
editing
editing
proposed
R. H. Hardin , Jan 26 2012
proposed
editing
editing
proposed
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
(Maxima)
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 */
approved
editing
_R. H. Hardin (rhhardin(AT)att.net) _ Jan 26 2012
editing
approved
R. H. Hardin, <a href="/A205338/b205338.txt">Table of n, a(n) for n = 1..210</a>