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A269585
Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by more than one.
1
32, 229, 964, 2969, 7456, 16237, 31844, 57649, 97984, 158261, 245092, 366409, 531584, 751549, 1038916, 1408097, 1875424, 2459269, 3180164, 4060921, 5126752, 6405389, 7927204, 9725329, 11835776, 14297557, 17152804, 20446889, 24228544
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = n^5 + 5*n^4 + 7*n^3 + 12*n^2 + 6*n + 1.
Conjectures from Colin Barker, Jan 24 2019: (Start)
G.f.: x*(32 + 37*x + 70*x^2 - 20*x^3 + 2*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
(End)
EXAMPLE
Some solutions for n=6:
..5. .4. .1. .6. .2. .4. .0. .4. .6. .6. .3. .6. .2. .1. .1. .0
..3. .2. .5. .6. .1. .0. .6. .5. .5. .2. .4. .3. .6. .1. .4. .4
..5. .4. .4. .0. .5. .1. .5. .1. .4. .4. .0. .2. .6. .2. .3. .6
..2. .2. .2. .2. .4. .2. .6. .6. .4. .5. .3. .1. .1. .2. .6. .5
..2. .0. .6. .0. .4. .4. .4. .1. .2. .6. .3. .0. .2. .6. .0. .4
CROSSREFS
Row 5 of A269583.
Sequence in context: A070053 A022146 A160061 * A199913 A301795 A301968
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 01 2016
STATUS
approved