cp's OEIS Frontend

A221569 Number of 0..4 arrays of length n with each element differing from at least one neighbor by something other than 1.

%I A221569 #13 Jun 04 2018 17:54:15
%S A221569 0,17,59,289,1293,5913,26911,122621,558547,2544357,11590169,52796369,
%T A221569 240501763,1095550873,4990531051,22733220441,103555975477,
%U A221569 471725515497,2148837489879,9788536778149,44589436230083,203116958964733
%N A221569 Number of 0..4 arrays of length n with each element differing from at least one neighbor by something other than 1.
%H A221569 R. H. Hardin, <a href="/A221569/b221569.txt">Table of n, a(n) for n = 1..210</a>
%H A221569 Robert Israel, <a href="/A221569/a221569.pdf">Maple-assisted proof of formula</a>
%F A221569 Empirical: a(n) = 5*a(n-1) -3*a(n-2) +a(n-3) +15*a(n-4) +3*a(n-5) for n>6.
%F A221569 Empirical g.f.: -x^2*(17-26*x+45*x^2+8*x^3+x^4) / ( -1+5*x-3*x^2+x^3+15*x^4+3*x^5 ). - _R. J. Mathar_, Jun 06 2013
%F A221569 Formula verified by _Robert Israel_, Jun 04 2018: see link.
%e A221569 Some solutions for n=6
%e A221569 ..4....2....2....2....3....4....2....2....4....0....3....2....0....4....4....4
%e A221569 ..4....2....4....4....0....4....0....0....0....0....3....4....0....4....1....2
%e A221569 ..2....1....0....1....0....4....2....1....3....0....0....3....3....2....0....2
%e A221569 ..0....4....3....1....4....1....4....4....1....0....0....0....3....2....0....2
%e A221569 ..3....3....0....1....0....2....0....2....0....4....3....2....4....4....3....1
%e A221569 ..1....3....3....3....3....2....0....0....4....0....0....4....0....4....3....3
%p A221569 f:= gfun:-rectoproc({a(n) = 5*a(n-1) -3*a(n-2) +a(n-3) +15*a(n-4) +3*a(n-5),seq(a(i)=[0, 17, 59, 289, 1293, 5913][i],i=1..6)},
%p A221569 a(n),remember):
%p A221569 map(f, [$1..50]); # _Robert Israel_, Jun 04 2018
%Y A221569 Column 4 of A221573.
%K A221569 nonn
%O A221569 1,2
%A A221569 _R. H. Hardin_, Jan 20 2013