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A222842 T(n,k) is the number of n X k 0..3 arrays with no more than floor(n*k/2) elements equal to at least one horizontal or vertical neighbor, with new values introduced in row major 0..3 order.

%I A222842 #10 Mar 31 2025 22:01:08
%S A222842 1,1,1,2,8,2,11,105,105,11,34,1585,4797,1585,34,131,23107,326408,
%T A222842 326408,23107,131,438,353631,15364848,70144361,15364848,353631,438,
%U A222842 2150,5338646,1077545438,15371324917,15371324917,1077545438,5338646,2150,7676
%N A222842 T(n,k) is the number of n X k 0..3 arrays with no more than floor(n*k/2) elements equal to at least one horizontal or vertical neighbor, with new values introduced in row major 0..3 order.
%C A222842 Table starts:
%C A222842 .....1..........1.............2..............11................34
%C A222842 .....1..........8...........105............1585.............23107
%C A222842 .....2........105..........4797..........326408..........15364848
%C A222842 ....11.......1585........326408........70144361.......15371324917
%C A222842 ....34......23107......15364848.....15371324917....10720259944904
%C A222842 ...131.....353631....1077545438...3410802057085.11000375151330544
%C A222842 ...438....5338646...52487425596.763478480305913
%C A222842 ..2150...81874696.3689615795056
%C A222842 ..7676.1252153841
%C A222842 .32491
%H A222842 R. H. Hardin, <a href="/A222842/b222842.txt">Table of n, a(n) for n = 1..60</a>
%e A222842 Some solutions for n=3 and k=4:
%e A222842 ..0..1..0..2....0..1..0..1....0..1..0..2....0..1..0..0....0..1..1..2
%e A222842 ..3..0..3..2....1..2..1..0....0..0..2..2....2..2..0..1....1..0..2..3
%e A222842 ..2..1..3..0....0..1..2..2....2..1..0..3....3..0..1..0....0..1..2..3
%Y A222842 Columns 1..4 are A222650, A222839, A222840, A222841.
%K A222842 nonn,tabl
%O A222842 1,4
%A A222842 _R. H. Hardin_, Mar 06 2013