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Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by more than one.
1

%I #8 Jan 24 2019 17:26:21

%S 128,1889,13946,67763,248324,745013,1927694,4453031,9406088,18482249,

%T 34214498,60251099,101688716,165466013,260822774,399829583,597993104,

%U 874942001,1255198538,1769040899,2453461268,3353224709,4522033886

%N Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by more than one.

%H R. H. Hardin, <a href="/A269587/b269587.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^7 + 7*n^6 + 11*n^5 + 35*n^4 + 28*n^3 + 42*n^2 + 5*n - 1.

%F Conjectures from _Colin Barker_, Jan 24 2019: (Start)

%F G.f.: x*(128 + 865*x + 2418*x^2 + 1919*x^3 - 116*x^4 - 129*x^5 - 46*x^6 + x^7) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%e Some solutions for n=4:

%e ..0. .0. .2. .1. .1. .2. .3. .0. .0. .0. .3. .3. .1. .0. .4. .4

%e ..4. .3. .2. .2. .0. .2. .1. .4. .2. .0. .3. .1. .1. .3. .1. .0

%e ..3. .1. .3. .4. .2. .4. .1. .2. .3. .0. .0. .4. .3. .2. .4. .1

%e ..3. .0. .4. .4. .1. .3. .2. .3. .2. .1. .2. .3. .2. .2. .2. .0

%e ..2. .4. .3. .2. .1. .1. .3. .1. .1. .1. .0. .0. .4. .2. .0. .0

%e ..4. .4. .1. .3. .4. .4. .0. .4. .3. .1. .1. .0. .0. .1. .4. .0

%e ..1. .2. .2. .0. .1. .2. .4. .1. .2. .1. .3. .1. .0. .0. .3. .0

%Y Row 7 of A269583.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 01 2016