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A221598
Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 1 or less.
1
64, 393, 1210, 2715, 5082, 8475, 13056, 18987, 26430, 35547, 46500, 59451, 74562, 91995, 111912, 134475, 159846, 188187, 219660, 254427, 292650, 334491, 380112, 429675, 483342, 541275, 603636, 670587, 742290, 818907, 900600, 987531, 1079862
OFFSET
1,1
COMMENTS
Row 6 of A221596.
LINKS
FORMULA
Empirical: a(n) = 27*n^3 + 108*n^2 - 252*n + 267 for n>3.
Conjectures from Colin Barker, Aug 09 2018: (Start)
G.f.: x*(64 + 137*x + 22*x^2 - 23*x^3 - 26*x^4 - 10*x^5 - 2*x^6) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>7.
(End)
EXAMPLE
Some solutions for n=6:
..0....2....0....4....1....5....5....4....0....3....5....4....5....0....2....3
..1....1....0....4....1....5....5....4....0....4....6....5....6....1....3....2
..6....3....4....4....2....4....2....1....5....5....4....0....6....1....2....1
..6....2....3....3....1....5....2....2....6....6....3....1....1....3....2....0
..0....5....1....1....3....5....3....4....1....2....5....0....2....4....4....4
..1....4....2....1....4....4....2....3....1....3....6....0....3....3....5....4
CROSSREFS
Cf. A221596.
Sequence in context: A228759 A220976 A249984 * A017618 A343724 A231841
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 20 2013
STATUS
approved