cp's OEIS Frontend

A221594 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 1 or less.

%I A221594 #9 Oct 19 2017 06:11:59
%S A221594 0,19,53,361,1593,8475,41401,210101,1047967,5267759,26387005,
%T A221594 132384353,663707187,3328545333,16690533369,83697779149,419705882541,
%U A221594 2104659535459,10553975797069,52923856787737,265391103246031,1330826582140067
%N A221594 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 1 or less.
%C A221594 Column 6 of A221596.
%H A221594 R. H. Hardin, <a href="/A221594/b221594.txt">Table of n, a(n) for n = 1..210</a>
%F A221594 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 A221594 Empirical g.f.: x^2*(19 - 23*x + 54*x^2 + 17*x^3 + 42*x^4 - 9*x^5 + 3*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 A221594 Some solutions for n=6
%e A221594 ..3....5....0....0....3....4....2....6....3....1....6....1....4....6....6....0
%e A221594 ..3....6....1....0....3....3....3....6....2....0....5....0....4....5....5....1
%e A221594 ..5....3....2....0....4....5....4....1....3....0....5....3....2....3....5....0
%e A221594 ..4....4....4....1....2....4....5....2....4....0....3....2....3....2....6....3
%e A221594 ..3....2....4....5....3....6....6....2....1....3....2....3....3....5....5....3
%e A221594 ..4....3....5....5....2....6....5....1....0....4....3....2....4....4....5....4
%K A221594 nonn
%O A221594 1,2
%A A221594 _R. H. Hardin_, Jan 20 2013