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%I #7 Jan 25 2019 16:49:52
%S 42,626,3816,15036,45590,115902,259476,527576,994626,1764330,2976512,
%T 4814676,7514286,11371766,16754220,24109872,33979226,47006946,
%U 63954456,85713260,113318982,147966126,191023556,244050696,308814450,387306842
%N Number of length-6 0..n arrays with no adjacent pair x,x+1 repeated.
%H R. H. Hardin, <a href="/A269659/b269659.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^6 + 6*n^5 + 15*n^4 + 14*n^3 + 3*n^2 + 3*n.
%F Conjectures from _Colin Barker_, Jan 25 2019: (Start)
%F G.f.: 2*x*(21 + 166*x + 158*x^2 + 17*x^4 - 2*x^5) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F (End)
%e Some solutions for n=3:
%e ..1. .3. .3. .1. .2. .0. .1. .2. .2. .0. .3. .2. .2. .0. .2. .2
%e ..1. .0. .3. .0. .2. .0. .1. .3. .2. .0. .2. .0. .1. .3. .1. .0
%e ..1. .2. .0. .0. .2. .2. .2. .0. .0. .0. .0. .3. .0. .2. .0. .2
%e ..2. .0. .1. .3. .2. .0. .3. .1. .2. .2. .1. .3. .0. .2. .2. .0
%e ..1. .0. .2. .0. .0. .3. .0. .1. .0. .2. .0. .1. .1. .0. .1. .1
%e ..3. .1. .2. .1. .2. .2. .0. .1. .3. .0. .2. .3. .2. .0. .2. .3
%Y Row 6 of A269656.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 02 2016
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