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A269641
Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.
1
9, 63, 221, 567, 1209, 2279, 3933, 6351, 9737, 14319, 20349, 28103, 37881, 50007, 64829, 82719, 104073, 129311, 158877, 193239, 232889, 278343, 330141, 388847, 455049, 529359, 612413, 704871, 807417, 920759, 1045629, 1182783, 1333001
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = n^4 + 4*n^3 + 3*n^2 + 2*n - 1.
Conjectures from Colin Barker, Jan 25 2019: (Start)
G.f.: x*(3 - x)*(3 + 7*x + x^2 + x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
EXAMPLE
Some solutions for n=3:
..3. .2. .1. .2. .0. .0. .3. .0. .1. .2. .1. .2. .3. .0. .3. .2
..1. .3. .2. .2. .3. .3. .2. .0. .0. .3. .0. .1. .1. .0. .0. .0
..3. .1. .0. .0. .0. .1. .0. .2. .0. .2. .0. .2. .3. .2. .1. .2
..3. .2. .0. .3. .0. .2. .1. .1. .2. .2. .3. .3. .1. .3. .0. .2
CROSSREFS
Row 4 of A269640.
Sequence in context: A085645 A299579 A344526 * A269410 A178161 A015669
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 02 2016
STATUS
approved