cp's OEIS Frontend

A221599 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 1 or less.

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