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A267960 Number of n X 1 0..2 arrays with every repeated value in every row and column greater than the previous repeated value.

%I A267960 #9 Feb 25 2018 15:14:44
%S A267960 3,9,24,63,159,394,957,2292,5419,12678,29385,67560,154215,349770,
%T A267960 788741,1769388,3950499,8782094,19445313,42898032,94315743,206709714,
%U A267960 451711869,984397108,2139750939,4639901334,10038505657,21672089592,46693408599
%N A267960 Number of n X 1 0..2 arrays with every repeated value in every row and column greater than the previous repeated value.
%C A267960 Column 1 of A267966.
%H A267960 R. H. Hardin, <a href="/A267960/b267960.txt">Table of n, a(n) for n = 1..210</a>
%F A267960 Empirical: a(n) = 6*a(n-1) - 9*a(n-2) - 8*a(n-3) + 24*a(n-4) - 16*a(n-6).
%F A267960 Conjectures from _Colin Barker_, Feb 25 2018: (Start)
%F A267960 G.f.: x*(3 - 9*x - 3*x^2 + 24*x^3 - 3*x^4 - 17*x^5) / ((1 + x)^2*(1 - 2*x)^4).
%F A267960 a(n) = (96*n + 2^n*(9*n*(n*(n+44)+445)+7622) + 640) / 7776 for n even.
%F A267960 a(n) = (2^n*(9*n*(n*(n+44)+445)+7622) - 32*(3*n+20)) / 7776 for n odd.
%F A267960 (End)
%e A267960 Some solutions for n=8:
%e A267960 ..1....0....1....1....0....2....0....0....2....1....1....1....2....0....2....0
%e A267960 ..2....1....0....1....2....1....2....2....2....2....2....0....0....2....1....1
%e A267960 ..0....0....2....2....0....1....0....1....1....0....2....1....1....1....0....1
%e A267960 ..2....0....1....2....1....2....2....0....0....2....0....1....0....2....1....0
%e A267960 ..0....1....1....0....2....1....0....0....2....0....2....0....2....0....1....2
%e A267960 ..1....2....0....1....1....2....0....1....0....1....1....2....0....2....0....0
%e A267960 ..2....0....2....0....0....1....2....2....2....0....0....2....1....0....2....1
%e A267960 ..2....2....2....2....0....0....2....0....1....1....2....0....2....2....0....2
%Y A267960 Cf. A267966.
%K A267960 nonn
%O A267960 1,1
%A A267960 _R. H. Hardin_, Jan 22 2016