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A221466
Number of 0..n arrays of length 7 with each element unequal to at least one neighbor, starting with 0.
1
8, 240, 1944, 8960, 30000, 81648, 192080, 405504, 787320, 1430000, 2459688, 4043520, 6397664, 9796080, 14580000, 21168128, 30067560, 41885424, 57341240, 77280000, 102685968, 134697200, 174620784, 223948800, 284375000, 357812208
OFFSET
1,1
COMMENTS
Row 7 of A221463.
LINKS
FORMULA
Empirical: a(n) = 1*n^6 + 4*n^5 + 3*n^4.
Conjectures from Colin Barker, Aug 05 2018: (Start)
G.f.: 8*x*(1 + 23*x + 54*x^2 + 14*x^3 - 2*x^4) / (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>7.
(End)
EXAMPLE
Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..6....4....5....2....5....2....4....4....4....4....1....3....4....6....2....3
..6....4....0....2....4....0....4....3....3....4....2....4....5....4....1....2
..0....5....6....4....0....4....2....6....3....5....2....6....2....6....6....1
..0....3....1....2....1....4....0....4....6....2....0....1....3....5....4....1
..6....6....1....3....0....3....2....4....6....0....2....0....6....4....4....0
..2....2....6....0....6....1....1....3....3....3....5....3....5....6....5....4
CROSSREFS
Cf. A221463.
Sequence in context: A240431 A222688 A254927 * A334712 A067360 A221770
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 17 2013
STATUS
approved