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A204034 Number of (n+1)X4 0..1 arrays with the sums of 2X2 subblocks nondecreasing rightwards and downwards.

%I A204034 #7 Jul 22 2025 17:43:09
%S A204034 121,603,2928,10505,37642,111578,330509,863435,2254026,5394662,
%T A204034 12906149,29037224,65337510,140736855,303340170,634000207,1326522462,
%U A204034 2717180447,5573314419,11270539628,22825534613,45808619416,92067615036,184020632660
%N A204034 Number of (n+1)X4 0..1 arrays with the sums of 2X2 subblocks nondecreasing rightwards and downwards.
%C A204034 Column 3 of A204039
%H A204034 R. H. Hardin, <a href="/A204034/b204034.txt">Table of n, a(n) for n = 1..210</a>
%F A204034 Empirical: a(n) = 4*a(n-1) +20*a(n-2) -98*a(n-3) -168*a(n-4) +1122*a(n-5) +674*a(n-6) -7970*a(n-7) -205*a(n-8) +39322*a(n-9) -13326*a(n-10) -142896*a(n-11) +86380*a(n-12) +395612*a(n-13) -325028*a(n-14) -850708*a(n-15) +867429*a(n-16) +1433880*a(n-17) -1752520*a(n-18) -1894178*a(n-19) +2759240*a(n-20) +1938970*a(n-21) -3430470*a(n-22) -1491450*a(n-23) +3380665*a(n-24) +795530*a(n-25) -2631230*a(n-26) -214060*a(n-27) +1599540*a(n-28) -65400*a(n-29) -744088*a(n-30) +104272*a(n-31) +255920*a(n-32) -56864*a(n-33) -61344*a(n-34) +17856*a(n-35) +9152*a(n-36) -3200*a(n-37) -640*a(n-38) +256*a(n-39)
%e A204034 Some solutions for n=4
%e A204034 ..1..0..0..0....1..1..0..0....1..0..1..1....0..0..1..1....0..0..0..0
%e A204034 ..0..0..1..0....0..0..1..1....0..1..1..0....1..1..0..0....0..1..0..1
%e A204034 ..0..1..1..1....1..1..1..1....1..0..1..1....0..0..1..1....1..1..1..1
%e A204034 ..0..1..1..1....0..0..1..1....0..1..1..1....1..1..0..0....1..0..1..0
%e A204034 ..1..1..1..1....1..1..1..1....0..1..1..1....0..0..1..1....1..1..1..1
%K A204034 nonn
%O A204034 1,1
%A A204034 _R. H. Hardin_ Jan 09 2012