

A209727


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.


7



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, 17, 14, 12, 12, 14, 17, 24, 32, 25, 18, 16, 14, 16, 18, 25, 32, 48, 33, 26, 20, 18, 18, 20, 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
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OFFSET

1,1


COMMENTS

Table starts
..2..3..4..6..8.12.16.24.32.48.64..96.128.192.256.384.512.768.1024.1536.2048
..3..4..5..7..9.13.17.25.33.49.65..97.129.193.257.385.513.769.1025.1537.2049
..4..5..6..8.10.14.18.26.34.50.66..98.130.194.258.386.514.770.1026.1538.2050
..6..7..8.10.12.16.20.28.36.52.68.100.132.196.260.388.516.772.1028.1540.2052
..8..9.10.12.14.18.22.30.38.54.70.102.134.198.262.390.518.774.1030.1542.2054
.12.13.14.16.18.22.26.34.42.58.74.106.138.202.266.394.522.778.1034.1546.2058
.16.17.18.20.22.26.30.38.46.62.78.110.142.206.270.398.526.782.1038.1550.2062
.24.25.26.28.30.34.38.46.54.70.86.118.150.214.278.406.534.790.1046.1558.2070


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..1512


FORMULA

Empirical for column k:
k=1: a(n) = 2*a(n2).
k=2..7: a(n) = a(n1) + 2*a(n2)  2*a(n3).


EXAMPLE

Some solutions for n=4, k=3
..2..1..2..1....0..2..0..1....1..2..0..2....0..1..0..2....2..1..2..1
..0..2..0..2....2..1..2..0....2..0..1..0....2..0..2..1....0..2..0..2
..1..0..1..0....0..2..0..1....1..2..0..2....0..1..0..2....1..0..1..0
..0..2..0..2....2..1..2..0....2..0..1..0....2..0..2..1....0..2..0..2
..1..0..1..0....0..2..0..1....1..2..0..2....0..1..0..2....2..1..2..1


CROSSREFS

Column 1 is A029744(n+1).
Diagonal is A027383.
Sequence in context: A300293 A316388 A029107 * A063123 A086333 A240792
Adjacent sequences: A209724 A209725 A209726 * A209728 A209729 A209730


KEYWORD

nonn,tabl


AUTHOR

R. H. Hardin, Mar 12 2012


STATUS

approved



