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%I #5 Dec 25 2013 11:11:37
%S 196316,9292808,426876528,19562241288,893326493316,40779627244572,
%T 1860744623018290,84899953913483407,3873501429344049400,
%U 176724495756544758956,8062812768583455896334,367854389640020762312297
%N Number of (n+2)X(1+2) 0..3 arrays with no increasing sequence of length 3 horizontally or diagonally downwards
%C Column 1 of A234393
%H R. H. Hardin, <a href="/A234389/b234389.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 56*a(n-1) -26586*a(n-3) +161889*a(n-4) +3740796*a(n-5) -30895097*a(n-6) -187582514*a(n-7) +2012131719*a(n-8) +3280745010*a(n-9) -59781770178*a(n-10) +7670618556*a(n-11) +904843980967*a(n-12) -892611508774*a(n-13) -7204612789531*a(n-14) +10892252119424*a(n-15) +28238885649127*a(n-16) -56684455395140*a(n-17) -35741928894200*a(n-18) +126732346860892*a(n-19) -78600993413254*a(n-20) -49070875873290*a(n-21) +298655389117913*a(n-22) -293555658109466*a(n-23) -337785457906071*a(n-24) +667877163621548*a(n-25) +51130515043723*a(n-26) -819092825116086*a(n-27) +288447456035056*a(n-28) +623846568417000*a(n-29) -349481101559952*a(n-30) -250500894094540*a(n-31) +143930821969264*a(n-32) +59962044402386*a(n-33) -10651618650630*a(n-34) -25341728141720*a(n-35) +5021619526216*a(n-36) +951607924424*a(n-37) -672240236280*a(n-38) +347138677736*a(n-39) -70314891768*a(n-40) +4321472928*a(n-41) +870029888*a(n-42) -350580992*a(n-43) +45079552*a(n-44)
%e Some solutions for n=1
%e ..1..1..3....1..1..1....2..1..1....1..1..3....1..3..0....1..2..3....1..3..2
%e ..2..3..0....0..0..0....0..0..3....1..1..0....0..3..1....1..2..0....3..2..3
%e ..0..2..3....3..3..1....3..2..3....2..2..0....2..3..1....3..0..1....3..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 25 2013
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