A221682 Number of 0..7 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

0, 2, 5, 44, 199, 1182, 6102, 33710, 180382, 980490, 5289023, 28634131, 154747076, 837016897, 4525504274, 24472972752, 132331839901, 715586695597, 3869459738102, 20923925463760, 113144565987295, 611822365490334

Offset

1,2

Comments

Column 7 of A221683.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) +3*a(n-2) -16*a(n-3) +65*a(n-4) -14*a(n-5) +23*a(n-6) +2*a(n-7) +8*a(n-8).

Empirical g.f.: x^2*(2 - 5*x + 13*x^2 - 4*x^3 + 5*x^4 + 2*x^5 + 2*x^6) / (1 - 5*x - 3*x^2 + 16*x^3 - 65*x^4 + 14*x^5 - 23*x^6 - 2*x^7 - 8*x^8). - Colin Barker, Oct 19 2017

Example

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

Crossrefs

Sequence in context: A225724 A333734 A163115 * A366406 A088309 A334252

Adjacent sequences: A221679 A221680 A221681 * A221683 A221684 A221685

Keyword

nonn

Author

R. H. Hardin, Jan 22 2013

Status

approved