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A220196 T(n,k) = Sum of neighbor maps: log base 2 of the number of n X k binary arrays indicating the locations of corresponding elements equal to the sum mod 2 of their horizontal and vertical neighbors in a random 0..1 n X k array.

%I A220196 #6 Apr 20 2021 12:24:14
%S A220196 1,1,1,3,4,3,4,4,4,4,4,8,9,8,4,6,9,12,12,9,6,7,12,12,12,12,12,7,7,12,
%T A220196 18,20,20,18,12,7,9,16,21,24,23,24,21,16,9,10,17,22,28,30,30,28,22,17,
%U A220196 10,10,20,27,32,31,36,31,32,27,20,10,12,20,30,32,39,42,42,39,32,30,20,12,13,24
%N A220196 T(n,k) = Sum of neighbor maps: log base 2 of the number of n X k binary arrays indicating the locations of corresponding elements equal to the sum mod 2 of their horizontal and vertical neighbors in a random 0..1 n X k array.
%C A220196 Table starts
%C A220196 ..1..1..3..4..4..6..7..7..9..10.10..12.13.13.15.16.16.18.19.19
%C A220196 ..1..4..4..8..9.12.12.16.17..20.20..24.25.28.28.32.33.36.36
%C A220196 ..3..4..9.12.12.18.21.22.27..30.30..36.39.40.45.48.48.54
%C A220196 ..4..8.12.12.20.24.28.32.32..40.44..48.52.52.60.64.68
%C A220196 ..4..9.12.20.23.30.31.39.44..50.51..60.64.69.71.80
%C A220196 ..6.12.18.24.30.36.42.42.54..60.66..72.78.84.90
%C A220196 ..7.12.21.28.31.42.49.54.63..70.70..84.91.96
%C A220196 ..7.16.22.32.39.42.54.64.71..80.86..96.97
%C A220196 ..9.17.27.32.44.54.63.71.73..90.98.108
%C A220196 .10.20.30.40.50.60.70.80.90.100
%C A220196 .10.20.30.44.51.66.70.86.98
%C A220196 .12.24.36.48.60.72.84.96
%H A220196 R. H. Hardin, <a href="/A220196/b220196.txt">Table of n, a(n) for n = 1..199</a>
%F A220196 Empirical for column k:
%F A220196 k=1: a(n) = a(n-1) +a(n-3) -a(n-4) increment period 3: 0 2 1
%F A220196 k=2: a(n) = a(n-1) +a(n-4) -a(n-5) increment period 4: 3 0 4 1
%F A220196 k=3: a(n) = a(n-1) +a(n-6) -a(n-7) increment period 6: 1 5 3 0 6 3
%F A220196 k=4: a(n) = a(n-1) +a(n-5) -a(n-6) increment period 5: 4 4 0 8 4
%F A220196 k=5: a(n) = a(n-3) +a(n-8) -a(n-11) increment period 24: 5 3 8 3 7 1 8 5 6 1 9 4 5 2 9 3 7 2 7 5 6 0 10 4
%F A220196 k=6: a(n) = a(n-1) +a(n-9) -a(n-10) increment period 9: 6 6 6 6 6 6 0 12 6
%F A220196 k=7: a(n) = a(n-1) +a(n-12) -a(n-13) increment period 12: 5 9 7 3 11 7 5 9 7 0 14 7
%e A220196 Some solutions for n=3 k=4
%e A220196 ..0..0..0..0....0..0..0..0....1..1..1..0....0..1..0..0....0..1..0..0
%e A220196 ..0..1..0..0....0..0..0..0....1..0..0..1....0..0..0..1....0..1..1..1
%e A220196 ..0..1..0..0....0..0..0..1....1..0..1..1....0..0..0..0....0..1..0..0
%Y A220196 Column 1 is A117571.
%K A220196 nonn,tabl
%O A220196 1,4
%A A220196 _R. H. Hardin_ Dec 07 2012