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A223041 T(n,k)=Number of nXk 0..3 arrays with no more than floor(nXk/2) elements equal to at least one horizontal, diagonal or antidiagonal neighbor, with new values introduced in row major 0..3 order.

%I A223041 #6 Jul 23 2025 03:25:00
%S A223041 1,1,2,2,8,5,11,98,105,15,34,1265,3780,1585,51,131,17356,229437,
%T A223041 255943,23107,187,438,241583,8580619,42964721,10904199,353631,715,
%U A223041 2150,3395532,545607733,7361951209,8206670940,751990800,5338646,2795,7676,48048796
%N A223041 T(n,k)=Number of nXk 0..3 arrays with no more than floor(nXk/2) elements equal to at least one horizontal, diagonal or antidiagonal neighbor, with new values introduced in row major 0..3 order.
%C A223041 Table starts
%C A223041 .....1........1...........2............11............34...........131
%C A223041 .....2........8..........98..........1265.........17356........241583
%C A223041 .....5......105........3780........229437.......8580619.....545607733
%C A223041 ....15.....1585......255943......42964721....7361951209.1278533695058
%C A223041 ....51....23107....10904199....8206670940.3829674402996
%C A223041 ...187...353631...751990800.1590576924149
%C A223041 ...715..5338646.33007705273
%C A223041 ..2795.81874696
%C A223041 .11051
%H A223041 R. H. Hardin, <a href="/A223041/b223041.txt">Table of n, a(n) for n = 1..49</a>
%e A223041 Some solutions for n=3 k=4
%e A223041 ..0..1..0..2....0..1..2..3....0..1..0..0....0..1..2..0....0..1..2..2
%e A223041 ..3..1..3..2....0..1..1..2....2..1..3..2....3..0..2..3....0..1..2..3
%e A223041 ..2..2..1..1....2..3..0..3....3..2..0..2....2..0..1..2....3..1..2..3
%Y A223041 Column 1 is A007581(n-1)
%Y A223041 Column 2 is A222839
%Y A223041 Row 1 is A222650
%K A223041 nonn,tabl
%O A223041 1,3
%A A223041 _R. H. Hardin_ Mar 12 2013