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 A243726 Number of length n+2 0..7 arrays with no three unequal elements in a row and no three equal elements in a row and new values 0..7 introduced in 0..7 order. 1

%I #12 Nov 03 2018 08:39:48

%S 3,6,12,25,53,116,259,594,1389,3323,8095,20113,50814,130631,341024,

%T 904241,2431805,6632342,18324521,51272228,145153079,415580431,

%U 1202307183,3512796459,10356995364,30795038625,92273776218,278450451781

%N Number of length n+2 0..7 arrays with no three unequal elements in a row and no three equal elements in a row and new values 0..7 introduced in 0..7 order.

%H R. H. Hardin, <a href="/A243726/b243726.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 90*a(n-3) + 105*a(n-4) + 441*a(n-5) - 652*a(n-6) - 1070*a(n-7) + 1491*a(n-8) + 1387*a(n-9) - 1198*a(n-10) - 840*a(n-11).

%F Empirical g.f.: x*(3 - 15*x - 30*x^2 + 211*x^3 + 103*x^4 - 1128*x^5 - 253*x^6 + 2756*x^7 + 852*x^8 - 2610*x^9 - 1371*x^10) / ((1 - 2*x)*(1 - x - x^2)*(1 - x - 3*x^2)*(1 - x - 4*x^2)*(1 - x - 5*x^2)*(1 - x - 7*x^2)). - _Colin Barker_, Nov 03 2018

%e Some solutions for n=6:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....1....1....1....0....0....1....0....1....1....1....1....0....1....0....0

%e ..1....0....1....1....1....1....0....1....1....1....1....0....1....1....1....1

%e ..1....0....0....0....1....0....1....0....0....2....0....0....1....2....1....1

%e ..2....1....0....0....0....0....0....1....1....2....1....1....0....2....2....2

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

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

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

%Y Column 7 of A243729.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 09 2014

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Last modified April 25 03:15 EDT 2024. Contains 371964 sequences. (Running on oeis4.)