cp's OEIS Frontend

A221682 Number of 0..7 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

%I A221682 #9 Oct 19 2017 07:41:30
%S A221682 0,2,5,44,199,1182,6102,33710,180382,980490,5289023,28634131,
%T A221682 154747076,837016897,4525504274,24472972752,132331839901,715586695597,
%U A221682 3869459738102,20923925463760,113144565987295,611822365490334
%N A221682 Number of 0..7 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.
%C A221682 Column 7 of A221683.
%H A221682 R. H. Hardin, <a href="/A221682/b221682.txt">Table of n, a(n) for n = 1..210</a>
%F A221682 Empirical: a(n) = 5*a(n-1) +3*a(n-2) -16*a(n-3) +65*a(n-4) -14*a(n-5) +23*a(n-6) +2*a(n-7) +8*a(n-8).
%F A221682 Empirical g.f.: x^2*(2 - 5*x + 13*x^2 - 4*x^3 + 5*x^4 + 2*x^5 + 2*x^6) / (1 - 5*x - 3*x^2 + 16*x^3 - 65*x^4 + 14*x^5 - 23*x^6 - 2*x^7 - 8*x^8). - _Colin Barker_, Oct 19 2017
%e A221682 Some solutions for n=6
%e A221682 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221682 ..0....0....0....1....0....0....1....1....0....0....1....1....1....1....0....0
%e A221682 ..0....4....0....6....1....7....7....1....2....0....1....0....1....5....0....6
%e A221682 ..2....3....1....7....2....6....6....3....2....1....2....0....3....4....6....5
%e A221682 ..1....3....1....2....6....0....3....2....3....6....2....1....3....1....5....6
%e A221682 ..2....2....1....3....7....1....3....2....2....6....3....0....2....2....5....7
%K A221682 nonn
%O A221682 1,2
%A A221682 _R. H. Hardin_, Jan 22 2013