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A185772 Number of (n+1)X3 0..2 arrays with no 2X2 subblock sum equal to any horizontal or vertical neighbor 2X2 subblock sum.

%I A185772 #7 Jul 22 2025 09:59:48
%S A185772 558,7074,89118,1151346,14837270,190416934,2442333998,31384892214,
%T A185772 403218559222,5178525140438,66503687019294,854217043141534,
%U A185772 10971879636716262,140921116729079306,1809957986000195766
%N A185772 Number of (n+1)X3 0..2 arrays with no 2X2 subblock sum equal to any horizontal or vertical neighbor 2X2 subblock sum.
%C A185772 Column 2 of A185777
%H A185772 R. H. Hardin, <a href="/A185772/b185772.txt">Table of n, a(n) for n = 1..200</a>
%F A185772 Empirical: a(n)=4*a(n-1)+49*a(n-2)+314*a(n-3)+6877*a(n-4)+3940*a(n-5)-66775*a(n-6)-5562*a(n-7)-4516042*a(n-8)-952177*a(n-9)+71657458*a(n-10)-81683756*a(n-11)+184951931*a(n-12)+934817466*a(n-13)-7278405891*a(n-14)+7577729242*a(n-15)+5409797117*a(n-16)-86907135378*a(n-17)+309915243239*a(n-18)-296185695772*a(n-19)-351845219222*a(n-20)+2892493385309*a(n-21)-6776522538782*a(n-22)+7058806126978*a(n-23)+3072790754210*a(n-24)-36661888510776*a(n-25)+74529700974096*a(n-26)-99999386996272*a(n-27)+60088842944712*a(n-28)+103959616747112*a(n-29)-313028645104464*a(n-30)+647329684563024*a(n-31)-801957721699232*a(n-32)+462840922316896*a(n-33)+384543021771136*a(n-34)-1781626290831168*a(n-35)+2738855357159040*a(n-36)-2209303681856256*a(n-37)-37689070540032*a(n-38)+2062920284706816*a(n-39)-2596060047154176*a(n-40)+2000380200560640*a(n-41)+81405399085056*a(n-42)-821157072150528*a(n-43)-122931731054592*a(n-44)+539315323600896*a(n-45)-332725569454080*a(n-46)+150115209707520*a(n-47)-33022594252800*a(n-48)
%e A185772 Some solutions for 5X3
%e A185772 ..0..0..1....0..0..1....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A185772 ..0..1..0....0..2..1....0..2..1....2..0..0....0..0..1....0..1..1....2..1..0
%e A185772 ..2..2..1....0..2..2....0..1..1....2..0..1....1..1..1....1..2..2....0..2..1
%e A185772 ..2..2..2....0..1..1....0..1..0....0..1..0....1..2..0....0..0..1....2..0..0
%e A185772 ..1..0..2....1..0..1....0..2..2....0..0..2....1..0..1....0..0..0....1..0..1
%K A185772 nonn
%O A185772 1,1
%A A185772 _R. H. Hardin_ Feb 03 2011