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

1,2

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Robert Israel, Maple-assisted proof of formula

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.

Example

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

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

Crossrefs

Column 4 of A221573.

Sequence in context: A176783 A086816 A243096 * A179816 A094207 A156912

Adjacent sequences: A221566 A221567 A221568 * A221570 A221571 A221572

Keyword

nonn

Author

R. H. Hardin, Jan 20 2013

Status

approved