

A268939


Number of lengthn 0..3 arrays with no repeated value unequal to the previous repeated value plus one mod 3+1.


1



4, 16, 60, 220, 788, 2780, 9684, 33404, 114292, 388444, 1312788, 4415548, 14790836, 49369628, 164279892, 545170172, 1804855540, 5962578652, 19661140116, 64722276796, 212738159924, 698312564636, 2289419181780, 7497612860540
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OFFSET

1,1


LINKS



FORMULA

Empirical: a(n) = 5*a(n1)  2*a(n2)  12*a(n3).
G.f.: 4*x*(1  x  3*x^2) / ((1  3*x)*(1  2*x  4*x^2)).
a(n) = (40*3^n + (2511*sqrt(5))*(1sqrt(5))^n + (1+sqrt(5))^n*(25+11*sqrt(5))) / 10.
(End)


EXAMPLE

Some solutions for n=9:
..3. .1. .0. .0. .2. .2. .0. .1. .2. .0. .2. .0. .2. .2. .2. .1
..0. .1. .2. .2. .0. .3. .3. .3. .0. .0. .1. .1. .0. .0. .1. .3
..2. .3. .3. .3. .1. .0. .2. .0. .0. .2. .3. .1. .3. .2. .3. .0
..0. .1. .3. .2. .3. .1. .1. .3. .2. .3. .1. .0. .1. .0. .0. .2
..2. .2. .0. .1. .1. .3. .2. .0. .3. .1. .3. .1. .3. .3. .1. .1
..2. .1. .3. .1. .2. .0. .2. .3. .2. .3. .2. .0. .2. .3. .2. .3
..1. .3. .0. .0. .3. .0. .0. .0. .3. .1. .3. .2. .0. .2. .1. .1
..2. .2. .1. .2. .2. .1. .2. .1. .1. .2. .1. .2. .1. .3. .1. .2
..0. .2. .0. .0. .0. .2. .1. .1. .3. .0. .1. .0. .3. .0. .3. .1


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



