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%I #4 Jan 12 2013 05:40:18
%S 1,1,2,3,4,3,4,6,4,4,4,8,9,8,5,6,10,12,12,9,6,7,12,12,12,15,12,7,7,14,
%T 18,20,20,18,12,8,9,16,21,24,24,24,21,16,9,10,18,22,28,30,30,28,24,17,
%U 10,10,20,27,32,35,30,31,32,27,20,11,12,22,30,32,39,42,42,40,32,30,20,12,13,24
%N T(n,k)=Sum of neighbor maps: log base 2 of the number of nXk binary arrays indicating the locations of corresponding elements equal to the sum mod 2 of their horizontal, diagonal and antidiagonal neighbors in a random 0..1 nXk array
%C Table starts
%C ..1..1..3..4..4..6..7..7..9.10.10.12.13.13.15.16.16.18
%C ..2..4..6..8.10.12.14.16.18.20.22.24.26.28.30.32.34
%C ..3..4..9.12.12.18.21.22.27.30.30.36.39.40.45.48
%C ..4..8.12.12.20.24.28.32.32.40.44.48.52.52.60
%C ..5..9.15.20.24.30.35.39.45.50.54.60.65.69
%C ..6.12.18.24.30.30.42.48.54.60.66.72.72
%C ..7.12.21.28.31.42.49.54.63.70.70.84
%C ..8.16.24.32.40.48.56.58.72.80.88
%C ..9.17.27.32.44.54.63.71.73
%C .10.20.30.40.50.60.70.80
%C .11.20.33.44.52.66.77
%C .12.24.36.48.60.72
%H R. H. Hardin, <a href="/A221356/b221356.txt">Table of n, a(n) for n = 1..161</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -a(n-2) increment period 1: 1
%F k=2: a(n) = a(n-1) +a(n-4) -a(n-5) increment period 4: 3 0 4 1
%F k=3: a(n) = 2*a(n-1) -a(n-2) increment period 1: 3
%F k=4: a(n) = a(n-1) +a(n-5) -a(n-6) increment period 5: 4 4 0 8 4
%F k=5: a(n) = a(n-1) +a(n-8) -a(n-9) increment period 8: 6 2 8 4 6 1 9 4
%F k=6: a(n) = a(n-1) +a(n-7) -a(n-8) increment period 7: 6 6 6 6 0 12 6
%F k=7: a(n) = 2*a(n-1) -a(n-2) increment period 1: 7
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-3) -a(n-4) increment period 3: 0 2 1
%F n=2: a(n) = 2*a(n-1) -a(n-2) increment period 1: 2
%F n=3: a(n) = a(n-1) +a(n-6) -a(n-7) increment period 6: 1 5 3 0 6 3
%F n=4: a(n) = a(n-1) +a(n-5) -a(n-6) increment period 5: 4 4 0 8 4
%F n=5: a(n) = a(n-1) +a(n-3) -a(n-4) increment period 3: 4 6 5
%F n=6: a(n) = a(n-1) +a(n-7) -a(n-8) increment period 7: 6 6 6 6 0 12 6
%e Some solutions for n=3 k=4
%e ..0..1..0..1....1..0..1..1....1..0..0..1....1..0..1..1....0..1..0..0
%e ..0..1..0..1....1..0..1..1....1..0..0..0....1..0..1..1....1..0..1..0
%e ..0..1..0..1....1..0..1..0....1..1..1..0....0..0..1..0....0..1..1..0
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Jan 12 2013
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