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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 19 2013
STATUS
approved