cp's OEIS Frontend

A221597 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 1 or less.

%I A221597 #8 Aug 09 2018 08:56:27
%S A221597 32,139,342,651,1068,1593,2226,2967,3816,4773,5838,7011,8292,9681,
%T A221597 11178,12783,14496,16317,18246,20283,22428,24681,27042,29511,32088,
%U A221597 34773,37566,40467,43476,46593,49818,53151,56592,60141,63798,67563,71436,75417,79506
%N A221597 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 1 or less.
%C A221597 Row 5 of A221596.
%H A221597 R. H. Hardin, <a href="/A221597/b221597.txt">Table of n, a(n) for n = 1..210</a>
%F A221597 Empirical: a(n) = 54*n^2 - 69*n + 63 for n>2.
%F A221597 Conjectures from _Colin Barker_, Aug 09 2018: (Start)
%F A221597 G.f.: x*(32 + 43*x + 21*x^2 + 10*x^3 + 2*x^4) / (1 - x)^3.
%F A221597 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.
%F A221597 (End)
%e A221597 Some solutions for n=6:
%e A221597 ..2....3....6....1....6....5....4....0....1....4....3....0....0....5....1....5
%e A221597 ..3....3....6....1....5....5....5....1....2....3....4....0....1....5....2....4
%e A221597 ..5....5....6....2....6....6....4....2....5....4....4....3....6....0....4....1
%e A221597 ..5....5....5....1....4....2....3....3....4....4....1....2....5....0....5....2
%e A221597 ..6....5....4....2....4....3....4....2....3....5....2....1....5....0....6....3
%Y A221597 Cf. A221596.
%K A221597 nonn
%O A221597 1,1
%A A221597 _R. H. Hardin_, Jan 20 2013