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A230739 T(n,k)=Number of (n+3)X(k+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

%I A230739 #6 Jul 23 2025 05:59:28
%S A230739 2,8,8,30,66,30,102,244,244,102,348,2016,2106,2016,348,1172,6576,
%T A230739 16536,16536,6576,1172,3956,54138,130446,320970,130446,54138,3956,
%U A230739 13326,173428,1025430,2382398,2382398,1025430,173428,13326,44916,1427040,8053490
%N A230739 T(n,k)=Number of (n+3)X(k+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.
%C A230739 Table starts
%C A230739 .....2.......8.......30........102..........348...........1172.............3956
%C A230739 .....8......66......244.......2016.........6576..........54138...........173428
%C A230739 ....30.....244.....2106......16536.......130446........1025430..........8053490
%C A230739 ...102....2016....16536.....320970......2382398.......46599682........342031378
%C A230739 ...348....6576...130446....2382398.....43853402......801845362......14669811856
%C A230739 ..1172...54138..1025430...46599682....801845362....36695929036.....625553036008
%C A230739 ..3956..173428..8053490..342031378..14669811856...625553036008...26681634560690
%C A230739 .13326.1427040.63237238.6692078688.268320990890.28644012159382.1137681116923966
%H A230739 R. H. Hardin, <a href="/A230739/b230739.txt">Table of n, a(n) for n = 1..199</a>
%F A230739 Empirical for column k:
%F A230739 k=1: a(n) = 3*a(n-1) +3*a(n-2) -6*a(n-3) +a(n-5)
%F A230739 k=2: a(n) = 31*a(n-2) -126*a(n-4) +42*a(n-6) +79*a(n-8) -a(n-10) +8*a(n-12)
%F A230739 k=3: [order 22]
%F A230739 k=4: [order 50]
%e A230739 Some solutions for n=3 k=4
%e A230739 ..x..0..x..0..x..2..x....x..0..x..2..x..2..x....x..0..x..0..x..1..x
%e A230739 ..1..x..1..x..1..x..0....2..x..1..x..0..x..1....1..x..1..x..2..x..0
%e A230739 ..x..2..x..0..x..1..x....x..0..x..1..x..1..x....x..2..x..0..x..2..x
%e A230739 ..1..x..0..x..2..x..0....1..x..0..x..2..x..0....1..x..0..x..2..x..0
%e A230739 ..x..2..x..1..x..1..x....x..2..x..0..x..2..x....x..2..x..1..x..1..x
%e A230739 ..1..x..1..x..0..x..0....1..x..2..x..1..x..1....1..x..0..x..0..x..0
%Y A230739 Column 1 is A230701
%Y A230739 Column 3 is A230703
%Y A230739 Column 5 is A230705
%Y A230739 Column 7 is A230707
%K A230739 nonn,tabl
%O A230739 1,1
%A A230739 _R. H. Hardin_, Oct 28 2013