A245158 - OEIS

%I #11 Nov 03 2018 10:32:27

%S 1,1,2,4,9,23,65,199,653,2275,8313,31439,121637,477307,1888721,

%T 7509799,29940861,119550419,477742889,1909988479,7637856725,

%U 30546970411,122178444417,488693854679,1954733475629,7818845822083,31275198738905

%N Number of length n 0..3 arrays with new values introduced in order from both ends.

%H R. H. Hardin, <a href="/A245158/b245158.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 37*a(n-2) + 64*a(n-3) - 52*a(n-4) + 16*a(n-5) for n>6.

%F Conjectures from _Colin Barker_, Nov 03 2018: (Start)

%F G.f.: x*(1 - 9*x + 29*x^2 - 43*x^3 + 31*x^4 - 11*x^5) / ((1 - x)^2*(1 - 2*x)^2*(1 - 4*x)).

%F a(n) = (-64 - 27*2^(2+n) + 4^n + 12*(32+3*2^n)*n) / 576 for n>1.

%F (End)

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

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

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

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

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

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

%Y Column 3 of A245163.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jul 12 2014