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A221574
Number of 0..n arrays of length 3 with each element differing from at least one neighbor by something other than 1.
1
2, 9, 26, 59, 114, 197, 314, 471, 674, 929, 1242, 1619, 2066, 2589, 3194, 3887, 4674, 5561, 6554, 7659, 8882, 10229, 11706, 13319, 15074, 16977, 19034, 21251, 23634, 26189, 28922, 31839, 34946, 38249, 41754, 45467, 49394, 53541, 57914, 62519, 67362
OFFSET
1,1
COMMENTS
Row 3 of A221573.
LINKS
FORMULA
Empirical: a(n) = 1*n^3 - 1*n^2 + 3*n - 1.
Conjectures from Colin Barker, Aug 08 2018: (Start)
G.f.: x*(2 + x)*(1 + x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3.
(End)
EXAMPLE
Some solutions for n=6:
..1....0....5....2....5....0....6....6....6....0....6....0....1....1....6....5
..6....5....1....4....3....5....4....6....4....4....1....4....1....3....2....1
..4....5....1....4....1....2....0....4....2....0....6....4....3....0....5....5
CROSSREFS
Cf. A221573.
Sequence in context: A218460 A085070 A083383 * A082289 A014150 A213387
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 20 2013
STATUS
approved