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Number of (n+1)X(3+1) 0..2 arrays with no 2X2 subblock having x11-x00 less than x10-x01
1

%I #4 Nov 29 2014 18:14:23

%S 867,17129,320950,6182747,119032248,2295692500,44280784440,

%T 854262466837,16480691222664,317958213164772,6134299936443854,

%U 118348278776443364,2283277183839898530,44051001079322901638,849870585415520935170

%N Number of (n+1)X(3+1) 0..2 arrays with no 2X2 subblock having x11-x00 less than x10-x01

%C Column 3 of A251065

%H R. H. Hardin, <a href="/A251060/b251060.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 20*a(n-1) +149*a(n-2) -3483*a(n-3) -1646*a(n-4) +181002*a(n-5) -200603*a(n-6) -4389443*a(n-7) +7563091*a(n-8) +57780280*a(n-9) -117969316*a(n-10) -443230440*a(n-11) +1006122140*a(n-12) +2058747657*a(n-13) -5162805928*a(n-14) -5921804997*a(n-15) +16838704214*a(n-16) +10500869967*a(n-17) -36121221195*a(n-18) -10740080874*a(n-19) +51975978543*a(n-20) +4392901894*a(n-21) -50615684360*a(n-22) +2927992450*a(n-23) +33382009991*a(n-24) -5129616183*a(n-25) -14828202384*a(n-26) +3221326394*a(n-27) +4390111165*a(n-28) -1132749541*a(n-29) -851993343*a(n-30) +240896502*a(n-31) +105264572*a(n-32) -31183216*a(n-33) -7839280*a(n-34) +2367008*a(n-35) +314880*a(n-36) -95232*a(n-37) -5120*a(n-38) +1536*a(n-39)

%e Some solutions for n=2

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 29 2014