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%I #7 Mar 21 2018 11:53:10
%S 4,96,1152,11424,103488,889056,7375872,59698464,474360768,3715826016,
%T 28777886592,220814937504,1681292682048,12718165610976,95670977133312,
%U 716203564928544,5338972029467328,39651633731043936,293513242790716032
%N Number of n X 2 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.
%C Column 2 of A269097.
%H R. H. Hardin, <a href="/A269091/b269091.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 14*a(n-1) -49*a(n-2) for n>3.
%F Conjectures from _Colin Barker_, Mar 21 2018: (Start)
%F G.f.: 4*x*(1 + 10*x + x^2) / (1 - 7*x)^2.
%F a(n) = 96*7^(n-3)*(5*n-3) for n>1.
%F (End)
%e Some solutions for n=4:
%e ..2..0. .2..2. .3..3. .3..3. .1..3. .3..3. .2..2. .3..2. .3..3. .1..3
%e ..1..1. .2..2. .2..3. .2..2. .3..1. .0..1. .3..2. .2..3. .3..3. .0..1
%e ..1..1. .1..0. .3..1. .1..3. .2..2. .1..0. .1..0. .0..1. .1..0. .0..2
%e ..3..3. .3..2. .2..2. .3..3. .3..3. .0..1. .1..2. .0..2. .3..2. .2..2
%Y Cf. A269097.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 19 2016
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