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A204033 Number of (n+1)X3 0..1 arrays with the sums of 2X2 subblocks nondecreasing rightwards and downwards.

%I A204033 #7 Jul 22 2025 17:43:02
%S A204033 44,164,603,1758,5130,13040,33223,77574,181559,401370,889157,1896644,
%T A204033 4052667,8444892,17621165,36165014,74299430,151007392,307137335,
%U A204033 620376066,1253727656,2522563936,5077320907,10191401694,20461362545
%N A204033 Number of (n+1)X3 0..1 arrays with the sums of 2X2 subblocks nondecreasing rightwards and downwards.
%C A204033 Column 2 of A204039
%H A204033 R. H. Hardin, <a href="/A204033/b204033.txt">Table of n, a(n) for n = 1..210</a>
%F A204033 Empirical: a(n) = 4*a(n-1) +8*a(n-2) -50*a(n-3) -9*a(n-4) +270*a(n-5) -128*a(n-6) -820*a(n-7) +709*a(n-8) +1520*a(n-9) -1824*a(n-10) -1722*a(n-11) +2797*a(n-12) +1070*a(n-13) -2696*a(n-14) -160*a(n-15) +1608*a(n-16) -240*a(n-17) -544*a(n-18) +160*a(n-19) +80*a(n-20) -32*a(n-21)
%e A204033 Some solutions for n=4
%e A204033 ..1..1..0....1..1..0....1..1..1....1..0..1....0..0..1....1..0..0....1..1..1
%e A204033 ..0..1..1....0..1..1....0..1..0....0..0..0....1..1..0....0..1..1....0..1..1
%e A204033 ..1..1..1....1..1..1....1..1..1....0..1..1....0..1..1....1..1..0....1..1..1
%e A204033 ..0..1..1....0..1..1....1..1..1....0..1..0....1..1..1....0..1..1....0..1..1
%e A204033 ..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..0....1..1..1
%K A204033 nonn
%O A204033 1,1
%A A204033 _R. H. Hardin_ Jan 09 2012