cp's OEIS Frontend

A221456 Number of 0..5 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..5 order.

%I A221456 #7 Aug 05 2018 08:23:17
%S A221456 0,1,2,7,25,102,455,2192,11203,59814,329343,1851911,10560334,60776590,
%T A221456 351887190,2045329031,11918417465,69563676328,406447507101,
%U A221456 2376416054328,13900548090293,81332697848104,475968841105687,2785759950405621
%N A221456 Number of 0..5 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..5 order.
%C A221456 Column 5 of A221459.
%H A221456 R. H. Hardin, <a href="/A221456/b221456.txt">Table of n, a(n) for n = 1..210</a>
%F A221456 Empirical: a(n) = 11*a(n-1) - 30*a(n-2) - 21*a(n-3) + 112*a(n-4) + 63*a(n-5) - 119*a(n-6) - 120*a(n-7) - 30*a(n-8).
%F A221456 Empirical g.f.: x^2*(1 - 9*x + 15*x^2 + 29*x^3 - 33*x^4 - 57*x^5 - 19*x^6) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 3*x - 3*x^2)*(1 - 5*x - 5*x^2)). - _Colin Barker_, Aug 05 2018
%e A221456 Some solutions for n=6:
%e A221456 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221456 ..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
%e A221456 ..2....2....0....2....2....1....2....2....0....1....1....2....2....2....0....2
%e A221456 ..2....1....0....2....0....0....1....1....2....0....2....2....0....3....2....3
%e A221456 ..3....3....2....0....3....0....0....1....1....2....3....1....0....4....0....3
%e A221456 ..2....4....3....3....0....2....1....2....0....1....1....3....1....0....2....4
%Y A221456 Cf. A221459.
%K A221456 nonn
%O A221456 1,3
%A A221456 _R. H. Hardin_, Jan 17 2013