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Number of length n 0..5 arrays with new values introduced in order from both ends.
1

%I #8 Nov 03 2018 12:09:47

%S 1,1,2,4,9,23,65,199,654,2296,8569,33825,140580,612890,2794159,

%T 13280627,65597882,335521900,1770176005,9593485125,53183385680,

%U 300371056446,1721926382427,9987133305239,58446578859494,344361988828048

%N Number of length n 0..5 arrays with new values introduced in order from both ends.

%H R. H. Hardin, <a href="/A245160/b245160.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 26*a(n-1) - 290*a(n-2) + 1820*a(n-3) - 7073*a(n-4) + 17618*a(n-5) - 28060*a(n-6) + 27480*a(n-7) - 14976*a(n-8) + 3456*a(n-9) for n>10.

%F Empirical g.f.: x*(1 - 25*x + 266*x^2 - 1578*x^3 + 5738*x^4 - 13236*x^5 + 19385*x^6 - 17565*x^7 + 9271*x^8 - 2381*x^9) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 4*x)^2*(1 - 6*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....1....1....1....1....1....1....1....0....1....0....1....1....1....1....0

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

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

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

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

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

%Y Column 5 of A245163.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jul 12 2014