A221594 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 1 or less.

0, 19, 53, 361, 1593, 8475, 41401, 210101, 1047967, 5267759, 26387005, 132384353, 663707187, 3328545333, 16690533369, 83697779149, 419705882541, 2104659535459, 10553975797069, 52923856787737, 265391103246031, 1330826582140067

Offset

1,2

Comments

Column 6 of A221596.

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*(19 - 23*x + 54*x^2 + 17*x^3 + 42*x^4 - 9*x^5 + 3*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
..3....5....0....0....3....4....2....6....3....1....6....1....4....6....6....0
..3....6....1....0....3....3....3....6....2....0....5....0....4....5....5....1
..5....3....2....0....4....5....4....1....3....0....5....3....2....3....5....0
..4....4....4....1....2....4....5....2....4....0....3....2....3....2....6....3
..3....2....4....5....3....6....6....2....1....3....2....3....3....5....5....3
..4....3....5....5....2....6....5....1....0....4....3....2....4....4....5....4

Crossrefs

Sequence in context: A072581 A242797 A142072 * A288144 A051871 A371110

Adjacent sequences: A221591 A221592 A221593 * A221595 A221596 A221597

Keyword

nonn

Author

R. H. Hardin, Jan 20 2013

Status

approved