A221523 Number of 0..7 arrays of length n with each element differing from at least one neighbor by 2 or more.

0, 42, 222, 1764, 12458, 90684, 654864, 4738970, 34274630, 247928860, 1793345580, 12971955294, 93830864024, 678713206224, 4909381705850, 35511361462492, 256866719859442, 1858011331955384, 13439678399558656, 97214130194552336

Offset

1,2

Comments

Column 7 of A221524.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +21*a(n-2) +58*a(n-3) +79*a(n-4) +32*a(n-5) +23*a(n-6) +4*a(n-7) +8*a(n-8).

Empirical g.f.: 2*x^2*(21 + 48*x + 108*x^2 + 34*x^3 + 36*x^4 + 12*x^6) / (1 - 3*x - 21*x^2 - 58*x^3 - 79*x^4 - 32*x^5 - 23*x^6 - 4*x^7 - 8*x^8). Colin Barker, Oct 18 2017

Example

Some solutions for n=6
..5....1....3....1....0....6....4....5....2....7....5....7....1....0....0....0
..3....4....7....6....3....3....6....2....5....3....0....5....6....4....3....4
..5....0....3....5....5....0....4....0....4....3....1....4....5....4....5....4
..6....0....1....1....0....4....7....2....2....5....6....7....3....7....7....2
..1....4....0....5....3....6....1....0....6....2....6....0....2....1....6....5
..4....6....2....7....0....0....3....6....2....5....0....7....6....5....3....1

Crossrefs

Sequence in context: A193394 A193390 A154472 * A263304 A116004 A221426

Adjacent sequences: A221520 A221521 A221522 * A221524 A221525 A221526

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved