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A230652 T(n,k)=Number of nXk 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

%I A230652 #6 Jun 02 2025 08:44:13
%S A230652 0,0,0,0,3,0,0,3,3,0,0,9,3,9,0,0,15,21,21,15,0,0,33,27,123,27,33,0,0,
%T A230652 63,177,531,531,177,63,0,0,129,231,2547,1635,2547,231,129,0,0,255,
%U A230652 1509,11745,28161,28161,11745,1509,255,0,0,513,1971,54957,90393,337977,90393
%N A230652 T(n,k)=Number of nXk 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).
%C A230652 Table starts
%C A230652 .0...0....0.....0.......0........0..........0...........0.............0
%C A230652 .0...3....3.....9......15.......33.........63.........129...........255
%C A230652 .0...3....3....21......27......177........231........1509..........1971
%C A230652 .0...9...21...123.....531.....2547......11745.......54957........255753
%C A230652 .0..15...27...531....1635....28161......90393.....1539207.......4956927
%C A230652 .0..33..177..2547...28161...337977....3951657....46564959.....547445439
%C A230652 .0..63..231.11745...90393..3951657...31908483..1374288243...11150938215
%C A230652 .0.129.1509.54957.1539207.46564959.1374288243.40860127671.1212230763441
%H A230652 R. H. Hardin, <a href="/A230652/b230652.txt">Table of n, a(n) for n = 1..337</a>
%F A230652 Empirical for column k:
%F A230652 k=1: a(n) = a(n-1)
%F A230652 k=2: a(n) = a(n-1) +2*a(n-2)
%F A230652 k=3: a(n) = 9*a(n-2) -4*a(n-4)
%F A230652 k=4: a(n) = 3*a(n-1) +8*a(n-2) -a(n-3) -a(n-4) for n>5
%F A230652 k=5: a(n) = 59*a(n-2) -230*a(n-4) -2*a(n-6) +32*a(n-8) for n>11
%F A230652 k=6: [order 23] for n>24
%F A230652 k=7: [order 46] for n>47
%e A230652 Some solutions for n=5 k=4
%e A230652 ..2..x..2..x....0..x..0..x....1..x..0..x....0..x..0..x....1..x..0..x
%e A230652 ..x..0..x..0....x..2..x..2....x..1..x..2....x..2..x..2....x..1..x..2
%e A230652 ..0..x..2..x....0..x..1..x....1..x..1..x....0..x..0..x....1..x..0..x
%e A230652 ..x..2..x..2....x..0..x..1....x..2..x..0....x..1..x..0....x..1..x..2
%e A230652 ..0..x..0..x....2..x..2..x....0..x..2..x....1..x..2..x....1..x..1..x
%Y A230652 Column 2 is A062510(n-1)
%K A230652 nonn,tabl
%O A230652 1,5
%A A230652 _R. H. Hardin_, Oct 27 2013