A221522 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 2 or more.

0, 30, 130, 900, 5368, 33380, 205080, 1264378, 7787228, 47975704, 295543282, 1820672982, 11216042008, 69095255496, 425653839018, 2622194869596, 16153749662332, 99513440156936, 613041859314376, 3776578532115986

Offset

1,2

Comments

Column 6 of A221524.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +14*a(n-2) +29*a(n-3) +28*a(n-4) +a(n-5) +27*a(n-6) +8*a(n-7) +2*a(n-8).

Empirical g.f.: 2*x^2*(15 + 20*x + 45*x^2 - 11*x^3 + 33*x^4 + 9*x^5 + 3*x^6) / (1 - 3*x - 14*x^2 - 29*x^3 - 28*x^4 - x^5 - 27*x^6 - 8*x^7 - 2*x^8). - Colin Barker, Oct 18 2017

Example

Some solutions for n=6
..0....1....6....1....0....6....4....1....3....3....1....4....2....1....5....6
..4....4....4....4....3....0....6....5....0....5....4....1....5....3....3....2
..3....3....0....2....2....4....2....0....6....0....1....5....6....1....5....2
..0....1....4....5....4....4....0....1....4....4....6....1....1....2....5....0
..0....0....0....4....0....2....6....6....3....5....0....0....2....6....2....2
..5....3....6....1....6....0....2....0....1....2....4....2....4....4....0....0

Crossrefs

Sequence in context: A307849 A044362 A044743 * A291582 A079588 A100147

Adjacent sequences: A221519 A221520 A221521 * A221523 A221524 A221525

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved