cp's OEIS Frontend

A221028 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, vertical and antidiagonal neighbors in a random 0..1 n X k array.

%I A221028 #6 Jul 18 2018 19:09:50
%S A221028 1,1,1,3,3,3,4,6,6,4,4,6,7,6,4,6,10,11,11,10,6,7,11,14,16,14,11,7,7,
%T A221028 13,17,20,20,17,13,7,9,16,19,21,24,21,19,16,9,10,16,24,27,30,30,27,24,
%U A221028 16,10,10,20,27,31,35,33,35,31,27,20,10,12,21,30,33,40,42,42,40,33,30,21,12,13
%N A221028 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, vertical and antidiagonal neighbors in a random 0..1 n X k array.
%C A221028 Table starts
%C A221028 ..1..1..3..4..4..6..7..7..9.10.10.12.13.13.15.16.16.18
%C A221028 ..1..3..6..6.10.11.13.16.16.20.21.23.26.26.30.31.33
%C A221028 ..3..6..7.11.14.17.19.24.27.30.30.36.39.42.43.47
%C A221028 ..4..6.11.16.20.21.27.31.33.40.44.47.50.56.60
%C A221028 ..4.10.14.20.24.30.35.40.42.48.55.59.62.69
%C A221028 ..6.11.17.21.30.33.42.46.54.60.66.71.75
%C A221028 ..7.13.19.27.35.42.45.53.62.69.72.83
%C A221028 ..7.16.24.31.40.46.53.63.69.79.87
%C A221028 ..9.16.27.33.42.54.62.69.81
%C A221028 .10.20.30.40.48.60.69.79
%C A221028 .10.21.30.44.55.66.72
%C A221028 .12.23.36.47.59.71
%H A221028 R. H. Hardin, <a href="/A221028/b221028.txt">Table of n, a(n) for n = 1..161</a>
%F A221028 Empirical for column k:
%F A221028 k=1: a(n) = a(n-1) +a(n-3) -a(n-4) increment period 3: 0 2 1
%F A221028 k=2: a(n) = a(n-1) +a(n-5) -a(n-6) increment period 5: 2 3 0 4 1
%F A221028 k=3: a(n) = a(n-1) +a(n-12) -a(n-13) increment period 12: 3 1 4 3 3 2 5 3 3 0 6 3
%F A221028 k=4: a(n) = a(n-1) +a(n-17) -a(n-18) increment period 17: 2 5 5 4 1 6 4 2 7 4 3 3 6 4 0 8 4
%F A221028 k=5: a(n) = a(n-1) +a(n-30) -a(n-31) increment period 30: 6 4 6 4 6 5 5 2 6 7 4 3 7 3 7 6 3 4 8 5 5 4 6 4 6 4 6 0 10 4
%e A221028 Some solutions for n=3 k=4
%e A221028 ..1..1..0..0....1..1..0..0....1..0..1..0....0..1..1..0....0..0..1..0
%e A221028 ..0..0..1..1....1..0..1..0....1..1..1..1....1..1..0..1....0..0..0..1
%e A221028 ..1..0..1..0....0..1..0..0....1..1..1..0....0..1..0..1....1..1..0..0
%Y A221028 Column 1 is A117571.
%K A221028 nonn,tabl
%O A221028 1,4
%A A221028 _R. H. Hardin_, Dec 29 2012