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A208872 T(n,k)=Number of nXk 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

%I A208872 #7 Jul 22 2025 21:32:56
%S A208872 1,2,2,5,12,5,15,136,143,15,51,1798,6520,1979,51,187,24472,307165,
%T A208872 324682,28246,187,715,334618,14493405,52947540,16205218,405481,715,
%U A208872 2795,4578580,683903931,8624977114,9130195864,808928836,5826959,2795,11051,62655190
%N A208872 T(n,k)=Number of nXk 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.
%C A208872 Table starts
%C A208872 ....1........2.............5................15.....................51
%C A208872 ....2.......12...........136..............1798..................24472
%C A208872 ....5......143..........6520............307165...............14493405
%C A208872 ...15.....1979........324682..........52947540.............8624977114
%C A208872 ...51....28246......16205218........9130195864..........5134914951163
%C A208872 ..187...405481.....808928836.....1574432811027.......3057224057476808
%C A208872 ..715..5826959...40380275500...271499374919883....1820216057105650386
%C A208872 .2795.83752328.2015711853262.46818078167209471.1083724145919960847502
%H A208872 R. H. Hardin, <a href="/A208872/b208872.txt">Table of n, a(n) for n = 1..160</a>
%e A208872 Some solutions for n=4 k=3
%e A208872 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..1..0
%e A208872 ..1..1..2....1..1..0....1..1..0....1..1..1....1..2..3....1..1..1....0..2..2
%e A208872 ..2..1..1....2..1..1....2..2..1....2..2..0....3..0..1....2..0..2....1..3..1
%e A208872 ..0..2..1....2..2..1....0..1..3....1..0..1....2..3..2....2..1..0....1..3..2
%Y A208872 Column 1 and row 1 are A007581(n-1)
%K A208872 nonn,tabl
%O A208872 1,2
%A A208872 _R. H. Hardin_ Mar 02 2012