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”).
%I #7 Aug 09 2018 08:56:37
%S 128,1113,4240,11011,22912,41401,67936,103975,150976,210397,283696,
%T 372331,477760,601441,744832,909391,1096576,1307845,1544656,1808467,
%U 2100736,2422921,2776480,3162871,3583552,4039981,4533616,5065915,5638336
%N Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 1 or less.
%C Row 7 of A221596.
%H R. H. Hardin, <a href="/A221599/b221599.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 243*n^3 - 351*n^2 + 237*n + 127 for n>2.
%F Conjectures from _Colin Barker_, Aug 09 2018: (Start)
%F G.f.: x*(128 + 601*x + 556*x^2 + 217*x^3 - 16*x^4 - 28*x^5) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.
%F (End)
%e Some solutions for n=6:
%e ..4....5....5....5....5....2....0....0....1....6....4....3....1....4....5....1
%e ..3....4....6....5....6....2....0....1....1....6....3....2....0....5....4....2
%e ..2....4....5....2....5....1....0....1....4....6....0....1....5....3....3....4
%e ..2....1....3....1....4....5....2....4....5....1....1....1....4....2....4....4
%e ..5....2....2....4....5....4....1....4....3....2....6....0....3....4....2....5
%e ..5....5....1....4....2....4....3....6....3....1....5....3....2....4....3....3
%e ..6....5....1....3....1....5....2....5....4....1....5....4....2....3....4....4
%Y Cf. A221596.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 20 2013