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%I #18 Jul 04 2016 03:56:26
%S 10,100,370,1970,9040,43990,209050,1002960,4793390,22944590,109759520,
%T 525189790,2512723030,12022412680,57521607650,275215898890,
%U 1316784620900,6300231318630,30143802148430,144224703156300,690051081572450
%N Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 0 and 1 0 1 vertically.
%C Row 4 of A207808.
%H Robert Israel and R. H. Hardin, <a href="/A207809/b207809.txt">Table of n, a(n) for n = 1..1460</a> (n = 1..210 from R. H. Hardin)
%H Robert Israel, <a href="/A207809/a207809.mpl.txt">Maple code to verify recursion</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,13,4,-12,1,1).
%F Empirical: a(n) = 2*a(n-1) +13*a(n-2) +4*a(n-3) -12*a(n-4) +a(n-5) +a(n-6)
%F From _Robert Israel_, Jul 03 2016: (Start)
%F The empirical recursion is true: see link for Maple verification.
%F G.f.: (10*x+80*x^2+40*x^3-110*x^4+10*x^5+10*x^6)/(1-2*x-13*x^2-4*x^3+12*x^4-x^5-x^6). (End)
%e Some solutions for n=4:
%e ..0..1..1..0....0..1..0..1....0..1..1..0....0..1..1..0....1..0..1..1
%e ..1..1..0..0....1..0..1..1....0..1..1..1....0..1..0..1....0..1..0..0
%e ..1..1..0..0....1..0..1..0....1..1..0..1....0..1..0..1....0..1..0..0
%e ..0..1..1..1....1..1..0..0....1..1..0..1....1..1..0..1....1..0..1..0
%p f:= gfun:-rectoproc({a(n)=2*a(n-1) +13*a(n-2) +4*a(n-3) -12*a(n-4) +a(n-5) +a(n-6), seq(a(i)=[10,100,370,1970,9040,43990][i],i=1..6)},a(n),remember):
%p map(f, [$1..50]); # _Robert Israel_, Jul 03 2016
%Y Cf. A207808.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 20 2012
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