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A269465
Number of length-n 0..6 arrays with no repeated value equal to the previous repeated value.
1
7, 49, 336, 2310, 15834, 108402, 741090, 5060706, 34523202, 235304034, 1602555906, 10906971810, 74188793154, 504367206882, 3427339028610, 23280526483746, 158079249910722, 1073053862250594, 7281968079533826, 49404973360789410
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 11*a(n-1) -18*a(n-2) -72*a(n-3).
Conjectures from Colin Barker, Jan 22 2019: (Start)
G.f.: 7*x*(1 - 4*x - 11*x^2) / ((1 - 6*x)*(1 - 5*x - 12*x^2)).
a(n) = (7/657)*2^(-4-n) * (-73*3^n*4^(1+n) + (949-103*sqrt(73))*(5-sqrt(73))^n + (5+sqrt(73))^n*(949+103*sqrt(73))).
(End)
EXAMPLE
Some solutions for n=6:
..4. .4. .2. .4. .4. .4. .5. .4. .3. .0. .6. .5. .0. .4. .2. .1
..5. .4. .2. .1. .2. .4. .6. .0. .2. .6. .4. .2. .6. .0. .4. .1
..3. .5. .4. .4. .2. .2. .6. .0. .1. .0. .0. .0. .6. .6. .6. .0
..6. .2. .3. .3. .4. .6. .0. .6. .0. .5. .4. .0. .3. .0. .0. .5
..3. .1. .5. .6. .2. .5. .3. .2. .5. .3. .1. .4. .6. .5. .3. .3
..5. .6. .0. .4. .0. .4. .2. .4. .1. .1. .1. .6. .0. .5. .3. .3
CROSSREFS
Column 6 of A269467.
Sequence in context: A269676 A269407 A269604 * A268455 A323559 A366925
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 27 2016
STATUS
approved