cp's OEIS Frontend

A221545 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by something other than 1, starting with 0.

%I A221545 #9 Aug 08 2018 09:07:43
%S A221545 8,134,1276,6311,22466,64047,156098,338711,672066,1242191,2167442,
%T A221545 3605703,5762306,8898671,13341666,19493687,27843458,38977551,53592626,
%U A221545 72508391,96681282,127218863,165394946,212665431,270684866,341323727
%N A221545 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by something other than 1, starting with 0.
%C A221545 Row 7 of A221542.
%H A221545 R. H. Hardin, <a href="/A221545/b221545.txt">Table of n, a(n) for n = 1..210</a>
%F A221545 Empirical: a(n) = 1*n^6 + 3*n^5 - 8*n^4 + 25*n^3 - 30*n^2 + 20*n - 9 for n>3.
%F A221545 Conjectures from _Colin Barker_, Aug 08 2018: (Start)
%F A221545 G.f.: x*(8 + 78*x + 506*x^2 - 87*x^3 + 675*x^4 - 822*x^5 + 572*x^6 - 279*x^7 + 79*x^8 - 10*x^9) / (1 - x)^7.
%F A221545 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>10.
%F A221545 (End)
%e A221545 Some solutions for n=6:
%e A221545 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221545 ..3....4....5....3....3....0....4....2....3....4....2....0....3....5....5....4
%e A221545 ..5....6....0....0....4....6....1....5....0....0....2....5....4....3....6....0
%e A221545 ..5....2....0....2....6....1....1....5....1....4....4....1....2....3....2....0
%e A221545 ..5....0....1....5....5....0....5....5....5....3....2....1....5....3....6....3
%e A221545 ..5....5....4....4....3....4....2....4....2....1....0....6....2....0....2....4
%e A221545 ..5....5....6....4....1....4....4....2....0....4....3....0....4....0....4....4
%Y A221545 Cf. A221542.
%K A221545 nonn
%O A221545 1,1
%A A221545 _R. H. Hardin_, Jan 19 2013