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

0, 17, 59, 289, 1293, 5913, 26911, 122621, 558547, 2544357, 11590169, 52796369, 240501763, 1095550873, 4990531051, 22733220441, 103555975477, 471725515497, 2148837489879, 9788536778149, 44589436230083, 203116958964733

Offset: 1

Author

R. H. Hardin, Jan 20 2013

Keywords

• nonn

Examples

			Some solutions for n=6
..4....2....2....2....3....4....2....2....4....0....3....2....0....4....4....4
..4....2....4....4....0....4....0....0....0....0....3....4....0....4....1....2
..2....1....0....1....0....4....2....1....3....0....0....3....3....2....0....2
..0....4....3....1....4....1....4....4....1....0....0....0....3....2....0....2
..3....3....0....1....0....2....0....2....0....4....3....2....4....4....3....1
..1....3....3....3....3....2....0....0....4....0....0....4....0....4....3....3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Robert Israel, Maple-assisted proof of formula

Crossrefs

Column 4 of A221573.

Programs

Maple

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)},
a(n),remember):
map(f, [$1..50]); # Robert Israel, Jun 04 2018

Formula

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.

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

Formula verified by Robert Israel, Jun 04 2018: see link.