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A269579
Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by more than one.
1
5, 25, 125, 613, 2969, 14239, 67763, 320495, 1508267, 7069055, 33020571, 153815099, 714838023, 3315709471, 15354722091, 71009625019, 328017083175, 1513765237255, 6980228317107, 32165146949139, 148133524803711, 681887792337519
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 16*a(n-1) - 93*a(n-2) + 220*a(n-3) - 112*a(n-4) - 192*a(n-5) - 2*a(n-6) + 8*a(n-7).
Empirical g.f.: x*(5 - 55*x + 190*x^2 - 162*x^3 - 154*x^4 + 4*x^5 + 6*x^6) / ((1 - 4*x)*(1 - 4*x - x^2)*(1 - 8*x + 14*x^2 + 8*x^3 - 2*x^4)). - Colin Barker, Jan 24 2019
EXAMPLE
Some solutions for n=6:
..3. .4. .0. .0. .0. .3. .0. .2. .2. .2. .4. .4. .1. .3. .1. .2
..1. .1. .3. .4. .4. .0. .4. .4. .3. .3. .2. .3. .4. .0. .0. .4
..3. .0. .4. .0. .2. .4. .1. .2. .4. .2. .0. .2. .0. .0. .1. .4
..4. .3. .0. .4. .3. .3. .0. .0. .2. .4. .3. .3. .1. .1. .0. .3
..4. .0. .2. .4. .2. .2. .4. .2. .2. .1. .1. .1. .1. .3. .4. .3
..4. .1. .0. .2. .4. .3. .0. .0. .0. .3. .3. .4. .4. .0. .4. .2
CROSSREFS
Column 4 of A269583.
Sequence in context: A228736 A126642 A269615 * A269431 A269686 A269490
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 01 2016
STATUS
approved