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A204035 Number of (n+1)X5 0..1 arrays with the sums of 2X2 subblocks nondecreasing rightwards and downwards.

%I A204035 #7 Jul 22 2025 17:43:16
%S A204035 286,1758,10505,44366,189580,642272,2198077,6415866,18855400,49463034,
%T A204035 130378965,316145840,769485458,1759764220,4037835608,8842012560,
%U A204035 19423451542,41206754874,87691553223,181894892784,378439038413
%N A204035 Number of (n+1)X5 0..1 arrays with the sums of 2X2 subblocks nondecreasing rightwards and downwards.
%C A204035 Column 4 of A204039
%H A204035 R. H. Hardin, <a href="/A204035/b204035.txt">Table of n, a(n) for n = 1..210</a>
%F A204035 Empirical: a(n) = 4*a(n-1) +26*a(n-2) -122*a(n-3) -302*a(n-4) +1766*a(n-5) +1978*a(n-6) -16138*a(n-7) -6930*a(n-8) +104454*a(n-9) +210*a(n-10) -509250*a(n-11) +151130*a(n-12) +1941310*a(n-13) -1020190*a(n-14) -5928050*a(n-15) +4236940*a(n-16) +14732870*a(n-17) -13009090*a(n-18) -30101870*a(n-19) +31422886*a(n-20) +50835986*a(n-21) -61498066*a(n-22) -71033438*a(n-23) +99090082*a(n-24) +81802994*a(n-25) -132597178*a(n-26) -76806422*a(n-27) +147941950*a(n-28) +57458666*a(n-29) -137661898*a(n-30) -32529638*a(n-31) +106500613*a(n-32) +11969534*a(n-33) -68049136*a(n-34) -652352*a(n-35) +35523824*a(n-36) -2735264*a(n-37) -14904960*a(n-38) +2248512*a(n-39) +4904928*a(n-40) -1052352*a(n-41) -1219328*a(n-42) +329216*a(n-43) +215296*a(n-44) -68608*a(n-45) -24064*a(n-46) +8704*a(n-47) +1280*a(n-48) -512*a(n-49)
%e A204035 Some solutions for n=4
%e A204035 ..0..0..0..1..1....0..0..1..1..1....1..1..1..0..0....1..0..1..1..0
%e A204035 ..0..0..0..1..0....0..1..0..1..1....0..0..0..1..1....0..1..0..1..1
%e A204035 ..0..0..1..1..1....0..1..1..1..1....1..1..1..0..1....1..1..1..1..1
%e A204035 ..0..0..0..1..1....0..1..1..1..1....1..0..1..1..1....1..1..1..1..1
%e A204035 ..0..1..1..1..1....0..1..1..1..1....1..1..1..0..1....1..1..1..1..1
%K A204035 nonn
%O A204035 1,1
%A A204035 _R. H. Hardin_ Jan 09 2012