A221545 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by something other than 1, starting with 0.

8, 134, 1276, 6311, 22466, 64047, 156098, 338711, 672066, 1242191, 2167442, 3605703, 5762306, 8898671, 13341666, 19493687, 27843458, 38977551, 53592626, 72508391, 96681282, 127218863, 165394946, 212665431, 270684866, 341323727

Offset

1,1

Comments

Row 7 of A221542.

Links

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

Formula

Empirical: a(n) = 1*n^6 + 3*n^5 - 8*n^4 + 25*n^3 - 30*n^2 + 20*n - 9 for n>3.

Conjectures from Colin Barker, Aug 08 2018: (Start)

G.f.: x*(8 + 78*x + 506*x^2 - 87*x^3 + 675*x^4 - 822*x^5 + 572*x^6 - 279*x^7 + 79*x^8 - 10*x^9) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>10.

(End)

Example

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

Crossrefs

Cf. A221542.

Sequence in context: A079912 A281948 A128287 * A316177 A003375 A007032

Adjacent sequences: A221542 A221543 A221544 * A221546 A221547 A221548

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved