A221681 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

0, 2, 5, 38, 166, 891, 4326, 21985, 109567, 551027, 2759757, 13846871, 69418237, 348143326, 1745704167, 8754189034, 43898170484, 220132165897, 1103869189670, 5535451646119, 27757983230949, 139194805502163, 698004183274703

Offset

1,2

Comments

Column 6 of A221683.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +5*a(n-2) -7*a(n-3) +33*a(n-4) +17*a(n-5) +24*a(n-6) -5*a(n-7) +2*a(n-8).

Empirical g.f.: x^2*(2 - 3*x + 8*x^2 + 3*x^3 + 6*x^4 - x^5 + x^6) / (1 - 4*x - 5*x^2 + 7*x^3 - 33*x^4 - 17*x^5 - 24*x^6 + 5*x^7 - 2*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
..1....0....0....1....0....0....1....1....1....0....1....1....0....1....0....0
..2....6....3....3....2....1....2....2....2....5....2....3....1....2....0....6
..0....6....3....2....3....5....3....2....1....5....0....3....0....1....3....6
..0....4....6....5....3....4....1....0....5....5....1....3....4....4....2....3
..0....3....5....6....2....3....2....1....5....6....2....3....5....4....1....2

Crossrefs

Sequence in context: A053609 A036780 A051501 * A347070 A290711 A228837

Adjacent sequences: A221678 A221679 A221680 * A221682 A221683 A221684

Keyword

nonn

Author

R. H. Hardin, Jan 22 2013

Status

approved