cp's OEIS Frontend

A221681 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

%I A221681 #9 Oct 19 2017 07:41:14
%S A221681 0,2,5,38,166,891,4326,21985,109567,551027,2759757,13846871,69418237,
%T A221681 348143326,1745704167,8754189034,43898170484,220132165897,
%U A221681 1103869189670,5535451646119,27757983230949,139194805502163,698004183274703
%N A221681 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.
%C A221681 Column 6 of A221683.
%H A221681 R. H. Hardin, <a href="/A221681/b221681.txt">Table of n, a(n) for n = 1..210</a>
%F A221681 Empirical: a(n) = 4*a(n-1) +5*a(n-2) -7*a(n-3) +33*a(n-4) +17*a(n-5) +24*a(n-6) -5*a(n-7) +2*a(n-8).
%F A221681 Empirical g.f.: x^2*(2 - 3*x + 8*x^2 + 3*x^3 + 6*x^4 - x^5 + x^6) / (1 - 4*x - 5*x^2 + 7*x^3 - 33*x^4 - 17*x^5 - 24*x^6 + 5*x^7 - 2*x^8). - _Colin Barker_, Oct 19 2017
%e A221681 Some solutions for n=6
%e A221681 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221681 ..1....0....0....1....0....0....1....1....1....0....1....1....0....1....0....0
%e A221681 ..2....6....3....3....2....1....2....2....2....5....2....3....1....2....0....6
%e A221681 ..0....6....3....2....3....5....3....2....1....5....0....3....0....1....3....6
%e A221681 ..0....4....6....5....3....4....1....0....5....5....1....3....4....4....2....3
%e A221681 ..0....3....5....6....2....3....2....1....5....6....2....3....5....4....1....2
%K A221681 nonn
%O A221681 1,2
%A A221681 _R. H. Hardin_, Jan 22 2013