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Number of length n 0..6 arrays with new values introduced in order from both ends.
1

%I #10 Nov 03 2018 12:09:52

%S 1,1,2,4,9,23,65,199,654,2296,8569,33825,140581,612933,2795181,

%T 13298407,65851100,338654554,1805083341,9952373825,56645932971,

%U 332111798479,2000990363889,12357518954759,78010845456554,501994699807228

%N Number of length n 0..6 arrays with new values introduced in order from both ends.

%H R. H. Hardin, <a href="/A245161/b245161.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 37*a(n-1) - 605*a(n-2) + 5765*a(n-3) - 35523*a(n-4) + 148371*a(n-5) - 427775*a(n-6) + 849335*a(n-7) - 1134976*a(n-8) + 969292*a(n-9) - 474720*a(n-10) + 100800*a(n-11) for n>12.

%F Empirical g.f.: x*(1 - 36*x + 570*x^2 - 5230*x^3 + 30829*x^4 - 122268*x^5 + 332049*x^6 - 616386*x^7 + 767435*x^8 - 616428*x^9 + 296529*x^10 - 69446*x^11) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 4*x)^2*(1 - 5*x)^2*(1 - 7*x)). - _Colin Barker_, Nov 03 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 6 of A245163.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jul 12 2014