|
%I #11 Apr 27 2020 02:30:41
%S 2,3,3,4,4,4,6,5,5,6,8,7,6,7,8,12,9,8,8,9,12,16,13,10,10,10,13,16,24,
%T 17,14,12,12,14,17,24,32,25,18,16,14,16,18,25,32,48,33,26,20,18,18,20,
%U 26,33,48,64,49,34,28,22,22,22,28,34,49,64,96,65,50,36,30,26,26,30,36,50,65,96
%N T(n,k) = 1/4 the number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
%C Table starts
%C ..2..3..4..6..8.12.16.24.32.48.64..96.128.192.256.384.512.768.1024.1536.2048
%C ..3..4..5..7..9.13.17.25.33.49.65..97.129.193.257.385.513.769.1025.1537.2049
%C ..4..5..6..8.10.14.18.26.34.50.66..98.130.194.258.386.514.770.1026.1538.2050
%C ..6..7..8.10.12.16.20.28.36.52.68.100.132.196.260.388.516.772.1028.1540.2052
%C ..8..9.10.12.14.18.22.30.38.54.70.102.134.198.262.390.518.774.1030.1542.2054
%C .12.13.14.16.18.22.26.34.42.58.74.106.138.202.266.394.522.778.1034.1546.2058
%C .16.17.18.20.22.26.30.38.46.62.78.110.142.206.270.398.526.782.1038.1550.2062
%C .24.25.26.28.30.34.38.46.54.70.86.118.150.214.278.406.534.790.1046.1558.2070
%H R. H. Hardin, <a href="/A209727/b209727.txt">Table of n, a(n) for n = 1..1512</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-2).
%F k=2..7: a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3).
%e Some solutions for n=4, k=3
%e ..2..1..2..1....0..2..0..1....1..2..0..2....0..1..0..2....2..1..2..1
%e ..0..2..0..2....2..1..2..0....2..0..1..0....2..0..2..1....0..2..0..2
%e ..1..0..1..0....0..2..0..1....1..2..0..2....0..1..0..2....1..0..1..0
%e ..0..2..0..2....2..1..2..0....2..0..1..0....2..0..2..1....0..2..0..2
%e ..1..0..1..0....0..2..0..1....1..2..0..2....0..1..0..2....2..1..2..1
%Y Column 1 is A029744(n+1).
%Y Diagonal is A027383.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Mar 12 2012
|
